Interest rates are 4.5% continuously compounded

The December 2026 (1 year) Copper $5 call costs $1.25

The December 2026 (1 year) Copper $5 put costs $2.75

What is spot?

Question

Interest rates are 4.5% continuously compounded

The December 2026 (1 year) Copper $5 call costs $1.25

The December 2026 (1 year) Copper $5 put costs $2.75

What is spot?

BlackTom AI · Accepted Answer

The task involves inferring the spot price S0 of the underlying asset using put-call parity for European options with continuous compounding. Since the problem provides r = 4.5% (continuous), T = 1 year, K = 5, C = 1.25, P = 2.75, and assumes no dividends, we can apply the parity relation: C - P = S0 e^{-δT} - K e^{-rT}. With δ = 0 (no dividends), this simplifies to C - P = S0 - K e^{-rT}.

First, evaluate the left-hand side: C - P = 1.25 - 2.75 = -1.50.
Next, compute the discounted strike: K e^{-rT} = 5 * e^{-0.045}. The exponential term e^{-0.045} is approximately 0.956, so 5 * e^{-0.045} ≈ 4.78.
Plug these into the parity equation and solve for S0: S0 = (C - P) + K e^{-rT} ≈ (-1.50) + 4.78 ≈ 3.28.

Therefore, the estimated spot price is about 3.28. If you check the arithmetic, the small differences from rounding e^{-0.045} will still yield a result near 3.28.

Notes on potential pitfalls: if one forgets the sign on (C - P) or miscalculates the discounted strike K e^{-rT}, the final S0 would be substantially off. Remember that the parity relationship ties together the prices of calls, puts, the spot, strike, and interest rates under no dividends, so each term has to be treated with the correct sign and the proper discount factor.

Regarding the input, there were no answer options provided to compare against, but the computation above shows how to derive S0 from the given data using standard put-call parity.

fin_412_120258_251367 Mid-term Test 2

Interest rates are 4.5% continuously compounded The December 2026 (1 year) Copper $5 call costs $1.25 The December 2026 (1 year) Copper $5 put costs $2.75 What is spot?

查看解析

登录即可查看完整答案

类似问题

Which relationship holds with the most precision?

Consider a put and a call on a stock with price S. The stock does not pay dividends. Interest rates are zero. Both options have the same expiration date. Between Monday and Tuesday, S does not change, but the call price falls by $2. What happens to the put price?

I am long Nasdaq futures because the financial conditions are ridiculously easy given all of the stimulus. However, we are going into earnings to I decide to buy a protective put. This means my synthetic position is

Which of the following can be used to create a long position in a European put option on a stock?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单