Exercise 8.4 This exercise will explore the relationship between risk and reward for a stock and a call option written on the same stock. We are in the Black-Scholes setting, under all the standard assumptions and notation. In particular, the stock price St is given by a geometric Brownian motion, dS et = u dt + o dW+, (8.14) where u, the instantaneous) mean rate of return, and o, the in- stantaneous) volatility, are given constants, and W = (W)t>o is a standard Brownian motion. A general concept in finance is that there is a trade-off between expected return (reward) and risk, and for our purposes, this involves the trade-off between u and o. We also have a European call option with strike K and expiration T that has terminal value CT = (ST K)+ and, at times t o is a standard Brownian motion. A general concept in finance is that there is a trade-off between expected return (reward) and risk, and for our purposes, this involves the trade-off between u and o. We also have a European call option with strike K and expiration T that has terminal value CT = (ST K)+ and, at times t