Answered step by step
Verified Expert Solution
Question
1 Approved Answer
3 Suppose you put together today the following portfolio: a long one call option on asset A (whose price today is So) with strike price
3 Suppose you put together today the following portfolio: a long one call option on asset A (whose price today is So) with strike price K and strike time T; b short one put option on the same asset, with strike price K and strike time T. How much did it cost you to put it together? That is, what is the value V of that portfolio? Suggestion. Normally, if Co and Po are the respective prices of the call and put options, the cost V of the portfolio can be computed directly as V = Co - P. Regrettably, we don't know yet how to compute Co and Po. Thus, I suggest to you the following indirect procedure. i Add to your portfolio a short position on a forward contract on asset A with maturity T. (The value today of the enlarged portfolio is still V since a forward contract is worth $0 the day it is issued.) ii Find the payoff at expiration of the enhanced portfolio and note that the payoff is deterministic. iii Thus, V must be the present value of that payoff. (User for the yearly interest rate applicable to that maturity and use the continu- ous compounding convention.) Your final answer must be an expression for V that involves So, K and r. 3 Suppose you put together today the following portfolio: a long one call option on asset A (whose price today is So) with strike price K and strike time T; b short one put option on the same asset, with strike price K and strike time T. How much did it cost you to put it together? That is, what is the value V of that portfolio? Suggestion. Normally, if Co and Po are the respective prices of the call and put options, the cost V of the portfolio can be computed directly as V = Co - P. Regrettably, we don't know yet how to compute Co and Po. Thus, I suggest to you the following indirect procedure. i Add to your portfolio a short position on a forward contract on asset A with maturity T. (The value today of the enlarged portfolio is still V since a forward contract is worth $0 the day it is issued.) ii Find the payoff at expiration of the enhanced portfolio and note that the payoff is deterministic. iii Thus, V must be the present value of that payoff. (User for the yearly interest rate applicable to that maturity and use the continu- ous compounding convention.) Your final answer must be an expression for V that involves So, K and r
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started