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english_1_1_r2
Buyers and sellers plan to trade a certain product. If the transaction is completed, the final price of the product will be p dollars. Initially, both the buyer's and the seller's valuation of the product are 0 dollars. The seller can choose to invest c dollars, thereby increasing the buyer's valuation of the product to v dollars (but this does not change the seller's valuation of the product; for the seller, the product's value remains 0 dollars). However, when deciding whether to invest, the seller does not know whether the buyer will subsequently purchase the product. Similarly, when the buyer decides whether to pay p dollars to purchase the product, they do not know whether the seller has already invested in the product. Assume the conditions: v > p > c > 0. The following table shows the payoff matrix of the game, where I, II, III, and IV represent the target cells. The numbers in parentheses indicate the respective payoffs: (buyer payoff, seller payoff). <image_1>
What should be filled in the cell marked I and II, respectively
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table
nan
nan
easy
open question
economics
english
1
1
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release_v2501
1
english_1_2_r2
nan
What should be filled in the cell marked III and IV, respectively
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table
nan
nan
easy
open question
economics
english
1
2
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release_v2501
2
english_1_3_r2
nan
Does this product transaction have a strictly dominant strategy? A strictly dominant strategy is one where, regardless of the opponent's strategy, there is always one strategy that yields a better payoff for the player.
null
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table
nan
nan
medium
open question
economics
english
1
3
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release_v2501
3
english_1_4_r2
nan
Does this product transaction have a strictly dominated strategy? A strictly dominated strategy is one where, regardless of the opponent's strategy, it always yields a worse payoff than another strategy for the player.
null
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table
nan
nan
medium
open question
economics
english
1
4
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release_v2501
4
english_1_5_r2
nan
By iteratively eliminating strictly dominated strategies, will the seller eventually invest in the product, and will the buyer purchase the product
null
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table
nan
nan
medium
open question
economics
english
1
5
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release_v2501
5
english_2_1_r2
On October 15, 2023, XXX Copper Plant and YYY Aluminum Plant reached a commodity swap cooperation agreement. According to the terms of the agreement, the two parties will conduct an equivalent exchange over a period of 5 months. Specifically, from November 2023 to March 2024, on the 15th of each month, XXX Copper Plant will deliver 10 tons of refined copper to YYY Aluminum Plant, while YYY Aluminum Plant will provide 35 tons of aluminum to XXX Copper Plant as an equivalent exchange. The table below shows the current quotes for each contract. The last four digits of the contract name represent the delivery month of the futures contract, e.g., '2312' represents delivery in December 2023. Assume the delivery date is the 15th of the delivery month. (Considering the time value of money, assume the risk-free annual interest rate is 1.8% from January to May.) <image_1>
Is this swap agreement fair? If yes, please return 0, If not, assuming XXX Copper Plant still delivers 10 tons of copper per month, how many tons of aluminum should YYY Aluminum Plant deliver each month to make it fair?
null
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table
nan
nan
medium
open question
derivatives
english
2
1
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release_v2501
6
english_3_1_r2
The following three figures (cut into three sections in chronological order) show the historical net value change curves of the two funds. <image_1> <image_2> <image_3>. For the following questions, assume returns are calculated using the logarithmic method and there are 250 trading days per year. Round all results to four decimal places.
What is the daily average return of Fund 1?
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table
nan
nan
medium
open question
portfolio management
english
3
1
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release_v2501
7
english_3_2_r2
nan
What is the standard deviation of daily returns of Fund 2?
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table
nan
nan
medium
open question
portfolio management
english
3
2
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release_v2501
8
english_3_3_r2
nan
Given an annual risk-free rate of 0.05%, what is the annual Sortino ratio of Fund 1's performance?
null
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table
nan
nan
medium
open question
portfolio management
english
3
3
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release_v2501
9
english_3_4_r2
nan
Given an annual risk-free rate of 0.03%, what is the daily sortino ratio of Fund 1's performance?
null
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table
nan
nan
hard
open question
portfolio management
english
3
4
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release_v2501
10
english_3_5_r2
nan
Given an annual risk-free rate of 0.01%, what is the annual Sharpe ratio of Fund 2's performance?
null
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table
nan
nan
medium
open question
portfolio management
english
3
5
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release_v2501
11
english_4_1_r2
Refer to the notation in <image_1>. The starting time it $t=0$ with initial forward price $F_0$.
Which one of the statement is correct about the lognormal assumption of forward rate
[ "A. Because $F_t$ is a martingale under $Q$, we assume $dF_t = \\sigma d W_t$", "B. Because $F_t$ is a martingale under $Q^T$, we assume $dF_t = \\sigma d W^T_t$", "C. Because $F_t$ is a martingale under $Q^T$, we assume $dF_t = \\sigma F_t d W^T_t$", "D. Because $F_t$ is a martingale under $Q$, we assume $dF_t = dt + \\sigma d W_t$" ]
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screenshot
nan
nan
easy
multiple-choice
derivatives
english
4
1
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release_v2501
12
english_4_2_r2
nan
Under the lognormal assumption, using $E$ denote the expectation, along with the notations in the context, the call option price at time $t$ can be written as $X* E max(F_T - K, 0)$, which one of the following statement is correct
[ "A. $X=DF(t, T)$ and the expectation is under the measure $Q$", "B. $X=DF(t, T)$ and the expectation is under the measure $Q^T$", "C. $X=exp(r_t * T)$ and the expectation is under the measure $Q^T$", "D. $X=DF(T, T)$ and the expectation is under the measure $Q^T$" ]
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screenshot
nan
nan
easy
multiple-choice
derivatives
english
4
2
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release_v2501
13
english_4_3_r2
nan
If we define a new probability $\widehat{Q}$ shown in <image_2>, denote $\widehat{W}_t$ as the brownian motion under $\widehat{Q}$, then express $F_T$ as a process driven by $ \widehat{W}$ with its initial price $F_0$.
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screenshot
nan
nan
hard
open question
derivatives
english
4
3
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release_v2501
14
english_4_4_r2
nan
Under the assumption of lognormal volatility of forward rate, derive the result of the expectation $E^T(max(F_T-K, 0)$ at time $t=0$ under measure $Q^T$
null
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screenshot
nan
nan
hard
open question
derivatives
english
4
4
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release_v2501
15
english_4_5_r2
nan
which statement is correct about the normal volatility assumption of forward rate
[ "A. Because $F_t$ is a martingale under $Q$, we assume $dF_t = \\sigma d W_t$", "B. Because $F_t$ is a martingale under $Q^T$, we assume $dF_t = \\sigma d W^T_t$", "C. Because $F_t$ is a martingale under $Q^T$, we assume $dF_t = \\sigma F_t d W^T_t$", "D. Because $F_t$ is a martingale under $Q$, we assume $dF_t = dt + \\sigma d W_t$" ]
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screenshot
nan
nan
easy
multiple-choice
derivatives
english
4
5
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release_v2501
16
english_4_6_r2
nan
Under the normal volatility assumption of forward rate, derive the result of the expectation $E^T(max(F_T-K, 0)$ at time $t=0$ under measure $Q^T$
null
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screenshot
nan
nan
hard
open question
derivatives
english
4
6
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release_v2501
17
english_4_7_r2
nan
Under the normal volatility assumption of forward rate, using $\sigma_{A}$ to denote the volatility of ATM call option, then express the price of the ATM call option at time $t<T$ as a function of $\sigma_{A}$
null
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screenshot
nan
nan
hard
open question
derivatives
english
4
7
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release_v2501
18
english_5_1_r2
In the given code block for the Black formula applied to swaptions (referenced as <image_1>),
what code should be inserted at line 14, currently indicated as <ans_1> in the figure?
null
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screenshot
nan
nan
easy
open question
fixed income
english
5
1
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release_v2501
19
english_5_2_r2
nan
what code should be inserted at line 19, currently indicated as <ans_2> in the figure?
null
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screenshot
nan
nan
easy
open question
fixed income
english
5
2
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release_v2501
20
english_5_3_r2
nan
what code should be inserted at line 31, currently indicated as <ans_3> in the figure?
null
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screenshot
nan
nan
easy
open question
fixed income
english
5
3
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release_v2501
21
english_5_4_r2
nan
what code should be inserted at line 33, currently indicated as <ans_4> in the figure?
null
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screenshot
nan
nan
medium
open question
fixed income
english
5
4
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release_v2501
22
english_5_5_r2
nan
Under what case will function "black_price" be broken, add a code block to fix it
null
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screenshot
nan
nan
hard
open question
fixed income
english
5
5
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release_v2501
23
english_5_6_r2
nan
Under what case will function "compute_delta" be broken, add a code block to fix it
null
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screenshot
nan
nan
hard
open question
fixed income
english
5
6
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release_v2501
24
english_6_1_r2
Consider the following FX quotes offered by two dealers, A and B. The forward quotes are in forward points. <image_1>. Round all numerical results to four decimal places in the following questions.
Is there any arbitrage opportunities on EURUSD spot?
[ "A. No", "B. one can earn 0.008 USD per EUR traded", "C. one can earn 0.0007 USD per EUR traded", "D. one can earn 0.0007 EUR per USD traded", "E. one can earn 0.0087 USD per EUR traded", "F. None of the above" ]
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table
nan
nan
medium
multiple-choice
fixed income
english
6
1
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release_v2501
25
english_6_2_r2
nan
Is there any arbitrage opportunities on USDCHF spot?
[ "A. No", "B. one can earn 0.0015 CHF per USD traded", "C. one can earn 0.0005 CHF per USD traded", "D. one can earn 0.0005 USD per CHF traded", "E. one can earn 0.0009 USD per CHF traded", "F. None of the above" ]
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table
nan
nan
medium
multiple-choice
fixed income
english
6
2
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release_v2501
26
english_6_3_r2
nan
what is the implied cross rate EURCHF from dealer A's quote in bid/ask form?
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table
nan
nan
hard
open question
fixed income
english
6
3
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release_v2501
27
english_6_4_r2
nan
Is there any triangular arbitrage opportunities between Deal A and B on EURCHF? If yes, please specify how to arbitrage, if no please respond 'no'.
null
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table
nan
nan
hard
open question
fixed income
english
6
4
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release_v2501
28
english_6_5_r2
nan
What is the 1M EURUSD quote from Dealer A, formatted the same way as the spot rate?
null
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table
nan
nan
easy
open question
fixed income
english
6
5
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release_v2501
29
english_6_6_r2
nan
What is the average annual forward premium on 1M EURUSD from Dealer A (Round the results to four decimals)
null
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table
nan
nan
easy
open question
fixed income
english
6
6
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release_v2501
30
english_7_1_r2
Consider the option position in <image_1>. Round all numerical results to four decimal places in the following questions.
Assuming no transaction cost, what is the implied volatility of this call option?
null
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table
nan
nan
easy
open question
derivatives
english
7
1
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release_v2501
31
english_7_2_r2
nan
Assuming no transaction cost, what is the delta of this call option?
null
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table
nan
nan
easy
open question
derivatives
english
7
2
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release_v2501
32
english_7_3_r2
nan
Given the Greeks in <image_2> for the call option and its corresponding put option, which share the same contract details except for the option type, identify any miscalculations in the table. If there are no errors, leave the response blank; otherwise, specify which Greek(s) is/are incorrect.
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table
nan
nan
medium
open question
derivatives
english
7
3
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release_v2501
33
english_7_4_r2
nan
Assume the option is exchange-traded and cash-settled, and upon settlement of an in-the-money (ITM) option, the buyer is subject to a stamp duty fee $c$ (applied as a multiplier to the spot price) when exercising the option. Additionally, assume that volatility remains constant at $\sigma$. Derive an explicit formula to describe the market price of the call option. Denote current underlying price as $S_t$ at time $t$, time to maturity $T$, strike $K$, risk free rate $r$.
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table
nan
nan
hard
open question
derivatives
english
7
4
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release_v2501
34
english_7_5_r2
nan
Based on context and the formula derived from the previous question, if the stamp duty fee is 0.01% and the volatility is a constant of 10%, then what is the trading price of this call option? Round the results to four decimals.
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table
nan
nan
hard
open question
derivatives
english
7
5
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release_v2501
35
english_3_6_nan
nan
Using historical method, what is daily VaR of Fund 2' returns at a 99% confidence level?
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table
nan
nan
hard
open question
portfolio management
english
3
6
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nan
36
chinese_1_1_r2
买家和卖家计划就某商品进行交易。如果交易达成,商品的成交价为 p 元。起初,该商品对于买家和卖家的价值评估均为 0 元。 <image_1> 卖家可以选择投入 c 元 进行投资,从而使买家对该商品的价值评估上升到 v 元(但不会改变卖家对该商品的价值评估,对卖家而言,该商品的价值仍然是 0 元)。然而,卖家在决定是否进行投资时,不知道买家是否会随后购买商品;同样地,买家在决定是否支付 p 元 购买商品时,也不知道卖家是否已经对该商品进行了投资。 假设条件为:v > p > c > 0。 下表展示了博弈的收益矩阵,其中 I, II, III, IV 分别标记了目标单位格,括号内的数字表示对应的收益:(买家收益,卖家收益)。
I 和 II 标记的单元格中应该分别填什么
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table
nan
nan
easy
open question
economics
chinese
1
1
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release_v2501
37
chinese_1_2_r2
nan
III 和 IV 标记的单元格中应该分别填什么
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table
nan
nan
easy
open question
economics
chinese
1
2
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release_v2501
38
chinese_1_3_r2
nan
该笔商品交易有严格占优策略(Dominant strategy)吗?严格占优策略是指不管对手采取什么策略,对自己来说,总有一种策略选择更为有利。
null
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table
nan
nan
medium
open question
economics
chinese
1
3
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release_v2501
39
chinese_1_4_r2
nan
该笔商品交易有严格劣策略(Dominated strategy)吗?严格劣策略是指不管对手策略如何变化,给自己带来的收益总是比另一种策略给自己带来的收益小的策略
null
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table
nan
nan
medium
open question
economics
chinese
1
4
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release_v2501
40
chinese_1_5_r2
nan
通过重复剔除严格劣策略,最终卖家是否会投资该商品以及买家是否会买入该商品?
null
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table
nan
nan
medium
open question
economics
chinese
1
5
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release_v2501
41
chinese_2_1_r2
2023年10月15日,XXX铜厂与YYY铝厂达成商品互换合作协议。根据协议条款,双方将开展为期5个月的等价交换。具体而言,自2023年11月起至2024年3月止,每月15日,XXX铜厂向YYY铝厂交付10吨精炼铜,同时YYY铝厂向XXX铜厂提供35吨铝作为对等交换。 下表为当前各个合约的报价。合约名称最后四个数字表示期货合约的交割月份,比如 ”2312“ 表示 23年12月交割。假设交割日为交割月份的15日。(考虑货币的时间价值,假设1-5月无风险年利率全部等于1.8%)。 <image_1>
该互换合约是否公允? 如果你认为该合约是公允合约的话,请输出0,如果不是公允合约的话,XXX铜厂同样每月支付10吨铜,YYY铝厂应支付多少吨铝才公平?
null
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table
nan
nan
medium
open question
derivatives
chinese
2
1
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release_v2501
42
chinese_3_1_r2
以下三张图片(按照时间顺序)分别是两个基金的净值收益率表格 <image_1> <image_2> <image_3>。 假设我们使用对数收益率,一年共 250个交易日。所有计算结果保留4位小数。
基金1 的日均收益率是多少
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table
nan
nan
medium
open question
portfolio management
chinese
3
1
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release_v2501
43
chinese_3_2_r2
nan
基金2 的日均收益率的方差是多少
null
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table
nan
nan
medium
open question
portfolio management
chinese
3
2
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release_v2501
44
chinese_3_3_r2
nan
在年化无风险利率为 0.05% 的情况下,基金 1 的年化 Sortino 比率是多少?
null
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table
nan
nan
medium
open question
portfolio management
chinese
3
3
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release_v2501
45
chinese_3_4_r2
nan
在年化无风险利率为 0.03% 的情况下,基金 1 的日度 Sortino 比率是多少?
null
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table
nan
nan
hard
open question
portfolio management
chinese
3
4
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release_v2501
46
chinese_3_5_r2
nan
在年化无风险利率为 0.01% 的情况下,基金 2 的年化 Sharpe 比率是多少?
null
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table
nan
nan
medium
open question
portfolio management
chinese
3
5
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release_v2501
47
chinese_3_6_r2
nan
使用历史数值法,基金 2 收益率在99%置信水平下的日VaR是多少?
null
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table
nan
nan
hard
open question
portfolio management
chinese
3
6
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release_v2501
48
chinese_4_1_r2
根据图中的变量说明,回答以下问题 <image_1>
关于远期利率对数正态波动率假设,以下哪个陈述是正确的?
[ "A. 因为 $F_t$ 测度 $Q$ 下的鞅, 所以我们可以假设 $dF_t = \\sigma d W_t$", "B. 因为 $F_t$ 是 测度 $Q^T$下的鞅, 所以我们可以假设 $dF_t = \\sigma d W^T_t$", "C. 因为 $F_t$ 是测度 $Q^T$下的鞅, 所以我们可以假设 $dF_t = \\sigma F_t d W^T_t$", "D. 因为 $F_t$ 是测度 $Q$下的鞅, 我们可以假设 $dF_t = dt + \\sigma d W_t$" ]
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screenshot
nan
nan
easy
multiple-choice
derivatives
chinese
4
1
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release_v2501
49
chinese_4_2_r2
nan
在远期利率对数正态波动率假设下,使用 $E$ 表示期望值,并结合上下文中的符号表示,时刻 $t$ 的看涨期权价格可以写为 $X* E max(F_T - K, 0)$, 以下哪个陈述是正确的?
[ "A. $X=DF(t, T)$ , 期望$E$是测度 $Q$下的期望", "B. $X=DF(t, T)$ ,期望$E$是测度 $Q^T$下的期望", "C. $X=exp(r_t * T)$, 期望$E$是测度 $Q^T$下的期望", "D. $X=DF(T, T)$,期望$E$是测度 $Q^T$下的期望" ]
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screenshot
nan
nan
easy
multiple-choice
derivatives
chinese
4
2
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release_v2501
50
chinese_4_3_r2
nan
如果我们定义一个新的概率测度$\widehat{Q}$ 在 <image_2> 中,用 $\widehat{W}_t$ 表示为 $\widehat{Q}$ 下的布朗运动,请将 $F_T$ 表示为由 $ \widehat{W}$ 驱动的过程,其初始价格为 $F_0$。
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screenshot
nan
nan
hard
open question
derivatives
chinese
4
3
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release_v2501
51
chinese_4_4_r2
nan
在远期利率对数正态波动率假设下,推导在测度$Q^T$下,$t=0$时刻 $E^T(max(F_T-K, 0)$ 的结果
null
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screenshot
nan
nan
hard
open question
derivatives
chinese
4
4
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release_v2501
52
chinese_4_5_r2
nan
关于远期利率正态波动率假设,以下哪个陈述是正确的?
[ "A. 因为 $F_t$ 是测度下 $Q$的鞅, 我们可以假设 $dF_t = \\sigma d W_t$", "B. 因为 $F_t$ 是测度 $Q^T$ 下的鞅, 我们假设 $dF_t = \\sigma d W^T_t$", "C. 因为 $F_t$ 是测度 $Q^T$ 下的鞅, 我们假设 $dF_t = \\sigma F_t d W^T_t$", "D. 因为 $F_t$ 是 $Q$ 下的鞅, 我们假设 $dF_t = dt + \\sigma d W_t$" ]
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screenshot
nan
nan
easy
multiple-choice
derivatives
chinese
4
5
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release_v2501
53
chinese_4_6_r2
nan
在远期利率正态波动率假设下,在测度 $Q^T$ 下,$t=0$时刻计算 期望$E^T(max(F_T-K, 0)$
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screenshot
nan
nan
hard
open question
derivatives
chinese
4
6
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release_v2501
54
chinese_4_7_r2
nan
在远期利率正态波动率假设下,使用$\sigma_{A}$ 表示$t$时刻 ATM 看涨期权的波动率,那么$t<T$时刻的看涨期权的价格的最简表达是什么
null
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screenshot
nan
nan
hard
open question
derivatives
chinese
4
7
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release_v2501
55
chinese_5_1_r2
在给定的应用于互换期权的Black公式代码块(参见<image_1>)中
在第14行(当前标记为<ans_1>)应该插入什么代码?
null
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nan
nan
easy
open question
fixed income
chinese
5
1
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release_v2501
56
chinese_5_2_r2
nan
在第19行(当前标记为<ans_2>)应该插入什么代码?
null
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screenshot
nan
nan
easy
open question
fixed income
chinese
5
2
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release_v2501
57
chinese_5_3_r2
nan
在第31行(当前标记为<ans_3>)应该插入什么代码?
null
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screenshot
nan
nan
easy
open question
fixed income
chinese
5
3
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release_v2501
58
chinese_5_4_r2
nan
在第33行(当前标记为<ans_4>)应该插入什么代码?
null
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nan
nan
medium
open question
fixed income
chinese
5
4
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release_v2501
59
chinese_5_5_r2
nan
在什么情况下函数black_price会出现问题?添加一个代码块来修复它。
null
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nan
nan
hard
open question
fixed income
chinese
5
5
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release_v2501
60
chinese_5_6_r2
nan
在什么情况下函数compute_delta会出现问题?添加一个代码块来修复它。
null
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nan
nan
hard
open question
fixed income
chinese
5
6
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release_v2501
61
chinese_6_1_r2
以下是两位交易商 A 和 B 提供的外汇报价。远期报价以远期点(forward points)表示。<image_1>
在 EURUSD 即期汇率上是否存在套利机会?
[ "A. 否", "B. 每交易 1 欧元可赚取 0.008 美元", "C. 每交易 1 欧元可赚取 0.0007 美元", "D. 每交易 1 美元可赚取 0.0007 欧元", "E. 每交易 1 欧元可赚取 0.0087 美元", "F. 以上都不是" ]
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table
nan
nan
medium
multiple-choice
fixed income
chinese
6
1
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release_v2501
62
chinese_6_2_r2
nan
在 USDCHF 即期汇率上是否存在套利机会?
[ "A. 否", "B. 每交易 1 美元可赚取 0.0015 瑞士法郎", "C. 每交易 1 美元可赚取 0.0005 瑞士法郎", "D. 每交易 1 瑞士法郎可赚取 0.0005 美元", "E. 每交易 1 瑞士法郎可赚取 0.0009 美元", "F. 以上都不是" ]
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table
nan
nan
medium
multiple-choice
fixed income
chinese
6
2
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release_v2501
63
chinese_6_3_r2
nan
根据交易商 A 的报价,计算 EURCHF 的隐含交叉汇率(买入价/卖出价形式)。
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table
nan
nan
hard
open question
fixed income
chinese
6
3
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release_v2501
64
chinese_6_4_r2
nan
在交易商 A 和 B 之间,EURCHF 是否存在三角套利机会
null
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table
nan
nan
hard
open question
fixed income
chinese
6
4
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release_v2501
65
chinese_6_5_r2
nan
根据交易商 A 的报价,1M EURUSD 的平均年化远期升水是多少?
null
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table
nan
nan
easy
open question
fixed income
chinese
6
5
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release_v2501
66
chinese_7_1_r2
考虑<image_1>中的期权头寸。以下问题中所有的数值结果请四舍五入到小数点后四位。
假设没有交易成本,计算该看涨期权的隐含波动率。
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table
nan
nan
easy
open question
derivatives
chinese
7
1
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release_v2501
67
chinese_7_2_r2
nan
假设没有交易成本,计算该看涨期权的Delta。
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table
nan
nan
easy
open question
derivatives
chinese
7
2
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release_v2501
68
chinese_7_3_r2
nan
根据<image_2>中的希腊字母,分别给出看涨期权和其对应的看跌期权的希腊字母值。两者的合同条款相同,仅期权类型不同,请找出表格中的任何计算错误。如果没有错误,请留空;如果有错误,请指定是哪个希腊字母不正确。
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table
nan
nan
medium
open question
derivatives
chinese
7
3
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release_v2501
69
chinese_7_4_r2
nan
假设该期权为交易所交易且现金结算,并且在执行该内在价值期权(ITM)时,买方需要支付一个印花税费$c$(该费用作为标的资产价格的乘数)。此外,假设波动率保持恒定为$\sigma$。推导出描述该看涨期权市场价格的显式公式。定义当前标的资产价格为$S_t$,到期时间为$T$,行权价为$K$,无风险利率为$r$。
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table
nan
nan
hard
open question
derivatives
chinese
7
4
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release_v2501
70
chinese_7_5_r2
nan
根据上下文以及前一个问题中推导的公式,如果印花税费为0.01%,且波动率恒定为10%,那么该看涨期权的交易价格是多少?请将结果四舍五入至小数点后四位。
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table
nan
nan
hard
open question
derivatives
chinese
7
5
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release_v2501
71
french_1_1_r2
Les acheteurs et les vendeurs prévoient de commercer un certain produit. Si la transaction est conclue, le prix final du produit sera de p dollars. Initialement, la valeur du produit est estimée à 0 dollar par les acheteurs comme par les vendeurs. Le vendeur peut choisir d'investir c dollars, augmentant ainsi la valeur du produit aux yeux de l'acheteur à v dollars (mais cela ne change pas la valeur du produit pour le vendeur ; pour le vendeur, la valeur du produit reste à 0 dollar). Cependant, lorsqu'il décide d'investir ou non, le vendeur ne sait pas si l'acheteur achètera le produit par la suite. De même, lorsque l'acheteur décide de payer p dollars pour acheter le produit, il ne sait pas si le vendeur a déjà investi dans le produit. Supposons les conditions suivantes : v > p > c > 0. Le tableau ci-dessous montre la matrice des gains du jeu, où I, II, III et IV représentent les cases cibles. Les chiffres entre parenthèses indiquent les gains respectifs : (gain de l'acheteur, gain du vendeur). <image_1>
Que faut-il remplir dans la case marquée I et II?
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table
nan
nan
easy
open question
economics
french
1
1
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release_v2501
72
french_1_2_r2
nan
Que faut-il remplir dans la case marquée III et IV ?
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table
nan
nan
easy
open question
economics
french
1
2
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release_v2501
73
french_1_3_r2
nan
Cette transaction sur le produit a-t-elle une stratégie strictement dominante ? Une stratégie strictement dominante est celle où, quelle que soit la stratégie de l'adversaire, il existe toujours une stratégie qui donne un meilleur gain au joueur.
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table
nan
nan
medium
open question
economics
french
1
3
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release_v2501
74
french_1_4_r2
nan
Cette transaction sur le produit a-t-elle une stratégie strictement dominée ? Une stratégie strictement dominée est celle où, quelle que soit la stratégie de l'adversaire, elle donne toujours un gain inférieur à celui d'une autre stratégie pour le joueur.
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table
nan
nan
medium
open question
economics
french
1
4
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release_v2501
75
french_1_5_r2
nan
En éliminant successivement les stratégies strictement dominées, le vendeur finira-t-il par investir dans le produit et l'acheteur achètera-t-il le produit ?
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table
nan
nan
medium
open question
economics
french
1
5
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release_v2501
76
french_2_1_r2
Le 15 octobre 2023, l'usine de cuivre XXX et l'usine d'aluminium YYY ont conclu un accord de coopération pour un échange de marchandises. Selon les termes de l'accord, les deux parties effectueront un échange équivalent sur une période de 5 mois. Plus précisément, de novembre 2023 à mars 2024, le 15 de chaque mois, l'usine de cuivre XXX livrera 10 tonnes de cuivre raffiné à l'usine d'aluminium YYY, tandis que l'usine d'aluminium YYY fournira 35 tonnes d'aluminium à l'usine de cuivre XXX en tant qu'échange équivalent. Le tableau ci-dessous montre les cotations actuelles pour chaque contrat. Les quatre derniers chiffres du nom du contrat représentent le mois de livraison du contrat à terme, par exemple, '2312' représente une livraison en décembre 2023. Supposons que la date de livraison soit le 15 du mois de livraison. (En prenant en compte la valeur temporelle de l'argent, supposons que le taux d'intérêt annuel sans risque soit de 1,8 % de janvier à mai.) <image_1>
Cet accord d'échange est-il équitable ? Si vous pensez que l'accord est équitable, veuillez répondre 0. Sinon, en supposant que l'usine de cuivre XXX livre toujours 10 tonnes de cuivre par mois, combien de tonnes d'aluminium l'usine d'aluminium YYY doit-elle livrer chaque mois pour que l'échange soit équitable ?
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nan
nan
medium
open question
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french
2
1
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release_v2501
77
french_3_1_r2
Les trois figures suivantes (divisées en trois sections dans l'ordre chronologique) montrent les courbes d'évolution de la valeur nette historique des deux fonds. <image_1> <image_2> <image_3>. Pour les questions suivantes, supposez que les rendements sont calculés selon la méthode logarithmique et qu'il y a 250 jours de trading par an. Arrondissez tous les résultats à quatre décimales.
Quel est le rendement moyen quotidien du Fonds 1 ?
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nan
nan
medium
open question
portfolio management
french
3
1
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release_v2501
78
french_3_2_r2
nan
Quelle est l'écart-type des rendements quotidiens du Fonds 2 ?
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table
nan
nan
medium
open question
portfolio management
french
3
2
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release_v2501
79
french_3_3_r2
nan
Étant donné un taux sans risque annuel de 0,05 %, quel est le ratio de Sortino annuel de la performance du Fonds 1 ?
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table
nan
nan
medium
open question
portfolio management
french
3
3
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release_v2501
80
french_3_4_r2
nan
Étant donné un taux sans risque annuel de 0,03 %, quel est le ratio de Sortino quotidien de la performance du Fonds 1 ?
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table
nan
nan
hard
open question
portfolio management
french
3
4
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release_v2501
81
french_3_5_r2
nan
Étant donné un taux sans risque annuel de 0,01 %, quel est le ratio de Sharpe annuel de la performance du Fonds 2 ?
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table
nan
nan
medium
open question
portfolio management
french
3
5
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release_v2501
82
french_3_6_r2
nan
En utilisant la méthode historique, quelle est la VaR quotidienne des rendements du Fonds 2 à un niveau de confiance de 99 % ?
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table
nan
nan
hard
open question
portfolio management
french
3
6
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release_v2501
83
french_4_1_r2
En se référant aux notations dans <image_1>. Le temps initial est $t=0$ avec un prix à terme initial $F_0$.
Laquelle des affirmations est correcte concernant l'hypothèse de log-normalité du taux à terme ?
[ "A. Parce que $F_t$ est une martingale sous $Q$, nous supposons $dF_t = \\sigma d W_t$", "B. Parce que $F_t$ est une martingale sous $Q^T$, nous supposons $dF_t = \\sigma d W ^T_t$", "C. Parce que $F_t$ est une martingale sous $Q^T$, nous supposons que $dF_t = \\sigma F_t d W^T_t$", "D. Parce que $F_t$ est une martingale sous $Q$, nous supposons que $dF_t = dt + \\sigma d W_t$" ]
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screenshot
nan
nan
easy
multiple-choice
derivatives
french
4
1
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release_v2501
84
french_4_2_r2
nan
Sous l'hypothèse de log-normalité, en utilisant $E$ pour représenter l'espérance et en se basant sur les notations du contexte, le prix d'une option d'achat au temps $t$ peut être écrit comme $X* E max(F_T - K, 0)$. Laquelle des affirmations suivantes est correcte ?
[ "$X=DF(t, T)$ et lespérance est sous la mesure $Q$, $X=DF(t", "T)$ et lespérance est sous la mesure $Q^T$", "$X=exp(r_t * T)$ et lespérance est sous la mesure $Q^T$, $X=DF(T", "T)$ et lespérance est sous la mesure $Q^T$" ]
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screenshot
nan
nan
easy
multiple-choice
derivatives
french
4
2
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release_v2501
85
french_4_3_r2
nan
Si nous définissons une nouvelle probabilité $\widehat{Q}$ montrée dans <image_2>, notons $\widehat{W}_t$ comme le mouvement brownien sous $\widehat{Q}$, puis exprimons $F_T$ comme un processus piloté par $ \widehat{W}$ avec son prix initial $F_0$.
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screenshot
nan
nan
hard
open question
derivatives
french
4
3
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release_v2501
86
french_4_4_r2
nan
Sous l'hypothèse de volatilité log-normale du taux à terme, dérivez le résultat de l'espérance $E^T(max(F_T-K, 0)$ sous la mesure $Q^T$
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screenshot
nan
nan
hard
open question
derivatives
french
4
4
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release_v2501
87
french_4_5_r2
nan
Quelle affirmation est correcte concernant l'hypothèse de volatilité normale du taux à terme ?
[ "A. Parce que $F_t$ est une martingale sous $Q$, nous supposons $dF_t = \\sigma d W_t$", "B. Parce que $F_t$ est une martingale sous $Q^T$, nous supposons $dF_t = \\sigma d W ^T_t$", "C. Parce que $F_t$ est une martingale sous $Q^T$, nous supposons que $dF_t = \\sigma F_t d W^T_t$", "D. Parce que $F_t$ est une martingale sous $Q$, nous supposons que $dF_t = dt + \\sigma d W_t$" ]
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screenshot
nan
nan
easy
multiple-choice
derivatives
french
4
5
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release_v2501
88
french_4_6_r2
nan
Sous l'hypothèse de volatilité normale du taux à terme, dérivez le résultat de l'espérance $E^T(max(F_T-K, 0)$ au moment $t=0$ sous la mesure $Q^T$
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screenshot
nan
nan
hard
open question
derivatives
french
4
6
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release_v2501
89
french_4_7_r2
nan
Dans l'hypothèse de volatilité normale du taux à terme, en utilisant $\sigma_{A}$ pour désigner la volatilité de l'option d'achat ATM, puis exprimer le prix de l'option d'achat ATM au moment $t<T$ en fonction de $\sigma_{ A}$
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screenshot
nan
nan
hard
open question
derivatives
french
4
7
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release_v2501
90
french_5_1_r2
Dans le bloc de code donné pour la formule de Black appliquée aux swaptions (référencé comme <image_1>) :
Quel code doit être inséré à la ligne 14, actuellement indiquée comme <ans_1> ?
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screenshot
nan
nan
easy
open question
fixed income
french
5
1
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release_v2501
91
french_5_2_r2
nan
Quel code doit être inséré à la ligne 19, actuellement indiquée comme <ans_2>
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screenshot
nan
nan
easy
open question
fixed income
french
5
2
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release_v2501
92
french_5_3_r2
nan
Quel code doit être inséré à la ligne 31, actuellement indiquée comme <ans_3>
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screenshot
nan
nan
easy
open question
fixed income
french
5
3
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release_v2501
93
french_5_4_r2
nan
Quel code doit être inséré à la ligne 33, actuellement indiquée comme <ans_4>
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screenshot
nan
nan
medium
open question
fixed income
french
5
4
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release_v2501
94
french_5_5_r2
nan
Dans quel cas la fonction "black_price" sera-t-elle défaillante ? Ajoutez un bloc de code pour la corriger.
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screenshot
nan
nan
hard
open question
fixed income
french
5
5
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release_v2501
95
french_5_6_r2
nan
Dans quel cas la fonction "compute_delta" sera-t-elle défaillante ? Ajoutez un bloc de code pour la corriger.
null
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screenshot
nan
nan
hard
open question
fixed income
french
5
6
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release_v2501
96
french_6_1_r2
Considérez les cotations FX suivantes proposées par deux dealers, A et B. Les cotations sur le forward sont exprimées en points de report. <image_1>
Y a-t-il des opportunités d’arbitrage sur le spot EURUSD ?
[ "Non", "on peut gagner 0,008 USD par EUR échangé", "on peut gagner 0,0007 USD par EUR échangé", "on peut gagner 0,0007 EUR par USD échangé", "on peut gagner 0,0087 USD par EUR échangé", "Aucune des réponses ci-dessus]" ]
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table
nan
nan
medium
multiple-choice
fixed income
french
6
1
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release_v2501
97
french_6_2_r2
nan
Y a-t-il des opportunités d’arbitrage sur le spot USDCHF ?
[ "Non", "on peut gagner 0,0015 CHF par USD échangé", "on peut gagner 0,0005 CHF par USD échangé", "on peut gagner 0,0005 USD par CHF échangé", "on peut gagner 0,0009 USD par CHF échangé", "Aucune des réponses ci-dessus" ]
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table
nan
nan
medium
multiple-choice
fixed income
french
6
2
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release_v2501
98
french_6_3_r2
nan
Quel est le taux de change croisé implicite EURCHF basé sur les cotations bid/ask du dealer A ?
null
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table
nan
nan
hard
open question
fixed income
french
6
3
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release_v2501
99
french_6_4_r2
nan
Existe-t-il des opportunités d’arbitrage triangulaire entre les dealers A et B sur l’EURCHF ?
null
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table
nan
nan
hard
open question
fixed income
french
6
4
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release_v2501

Introduction

FAMMA is a multi-modal financial Q&A benchmark dataset. The questions encompass three heterogeneous image types - tables, charts and text & math screenshots - and span eight subfields in finance, comprehensively covering topics across major asset classes. Additionally, all the questions are categorized by three difficulty levels — easy, medium, and hard - and are available in three languages — English, Chinese, and French. Furthermore, the questions are divided into two types: multiple-choice and open questions.

More importantly, FAMMA provides a "live" benchmark for evaluating financial analysis capabilities of LLMs. The benchmark continuously collects new questions from real-world financial professionals, ensuring up-to-date and contamination-free evaluation.

The leaderboard is regularly updated and can be accessed at https://famma-bench.github.io/famma/.

The project code is available at https://github.com/famma-bench/bench-script.

NEWS

🔥 Latest Updates:

Dataset Versions

FAMMA is continuously updated with new questions. We provide different versions of the dataset:

  • release_v2406: The release containing 1935 questions, collected from online sources. Apart from the questions, both answers and explanations are provided.
  • release_v2501: The release containing 100 questions, created by invited experts. Only the questions are provided.

Dataset Structure

  • idx:a unique identifier for the index of the question in the dataset.
  • question_id: a unique identifier for the question across the whole dataset: {language}{main_question_id}{sub_question_id}_{release_version}.
  • context: relevant background information related to the question.
  • question: the specific query being asked.
  • options: the specific query being asked.
  • image_1- image_7: directories of images referenced in the context or question.
  • image_type: type of the image, e.g., chart, table, screenshot.
  • answers: a concise and accurate response. (public on release v2406, non-public on the live set release v2501)
  • explanation:a detailed justification for the answer. (public on release v2406, non-public on the live set release v2501)
  • topic_difficulty: a measure of the question's complexity based on the level of reasoning required.
  • question_type: categorized as either multiple-choice or open-ended.
  • subfield: the specific area of expertise to which the question belongs, categorized into eight subfields.
  • language:the language in which the question text is written.
  • main_question_id:a unique identifier for the question within its context; questions with the same context share the same ID.
  • sub_question_id:a unique identifier for the question within its corresponding main question.
  • ans_image_1 - ans_image_6: (public on release v2406, non-public on the live set release v2501)

Download

see the script at https://github.com/famma-bench/bench-script/blob/main/step_1_download_dataset.py

Citation

If you use FAMMA in your research, please cite our paper as follows:

@article{xue2024famma,
  title={FAMMA: A Benchmark for Financial Domain Multilingual Multimodal Question Answering},
  author={Siqiao Xue, Tingting Chen, Fan Zhou, Qingyang Dai, Zhixuan Chu, and Hongyuan Mei},
  journal={arXiv preprint arXiv:2410.04526},
  year={2024},
  url={https://arxiv.org/abs/2410.04526}
}
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