This problem is based on the fundamental option pricing formula for the continuous-timemodel developed in class, namely the value at time 0 of an option with maturity T andpayoff F is given by:We consider the two options below:Fo=-rT= eEq[F].1A. An option with which you must buy a share of stock at expiration T = 1 for strikeprice K = So.B. An option with which you must buy a share of stock at expiration T = 1 for strikeprice K given byTK =TSt dt.(Note that both options can have negative payoffs.) We use the continuous-time Black-Scholes model to price these options. Assume that the interest rate on the money marketis r.(a) Using the fundamental option pricing formula, find the price of option A. (Hint:use the martingale properties developed in the lectures for the stock price processin order to calculate the expectations.)(b) Using the fundamental option pricing formula, find the price of option B.(c) Assuming the interest rate is very small (r ~0), use Taylor expansions to find thefirst order approximation in r of the two results in (a) and (b).(d) Can we intuitively explain the relationship between the two formulas obtained inpart (c) ?

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Answered: This problem is based on the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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