Question

— The stock’s price S is $100. After three months, it either goes up and gets multiplied by the factor U = 1.13847256, or it goes down and gets multiplied by the factor D = 0.88664332. — Options mature after T = 0.5 year and have a strike price of K = $105. — The continuously compounded risk-free interest rate r is 5 percent per year. — Today’s European call price is c and the put price is p. Call prices after one period are denoted by cU in the up node and cD in the down node. Call prices after two periods are denoted by cUD in the “up, and then down node” and so on. Put prices are similarly defined. To create the arbitrage-free synthetic call today, you need to:

Group of answer choices

buy 0.9343 shares of the stock and short sell 93.2677 units of the money market account

buy 0.8585 shares of the stock and short sell 42.2642 units of the money market account

buy 0.4827 shares of the stock and short sell 42.2642 units of the money market account

buy 0.8585 shares of the stock and short sell 85.5777 units of the money market account

please provide explanation

Answer 1

FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

Hedge Ratio = (Cu-Cd)/(Up-Dp)= 0.4827

Buy this many(0.4827) shares.  

Ans: buy 0.4827 shares of the stock and short sell 42.2642 units of the money market account.