The price of a certain security follows a geometric Brownian motion withdrift parameter = 0:05 and volatility parameter = 0:3. The presentprice of the security is 95.

i. If the interest rate is 4%, nd the no-arbitrage cost of a call optionthat expires in three months and has exercise price 100.

ii. What is the probability that the call option in part (a) is worthlessat the time of expiration?

iii. Suppose that a new type of investment on the security is beingtraded. This investment returns 50 at the end of one year if theprice six months after purchasing the investment is at least 105 andthe price one year after purchase is at least as much as the pricewas after six months. Determine the no-arbitrage cost of this

investment.