Derivatives

1. You try to price the options on XYZ Corp. The current stock price of XYZ is $100/share. The risk-free rate is 5%. You project the stock price of XYZ will either be $90 or $120 in a year. Assume you can borrow or lend money at the risk-free rate. Use risk-neutral approach to price the 1-year call and 1-year put option on XYZ Corp with the strike price of $105.

My Answer:

Step 1

U=120/120=1.2

D=90/100=0.90

Step 2

1+r-d)(u-d)=(1+5%-0.90)/(1.2-0.9)-0.5

Step 3

(0.5*15+0.5*0)/1.05=.142857 first value

Step 4

(0.5*0+0.5*15)1.05+7.142857 2nd value

2. Fisher Black and Myron Scholes receive the 1997 Nobel Prize in Economic Science for their work on option pricing. Although the model is theoretically elegant and beautiful, it was not widely used to price options in real life because it calls for inherent volatility which is unobservable. However, given the dependability of risk-neutral approach, people today normally use risk-neutral approach to price the options first, then they employ Black-Scholes model to estimate the implied volatility. Based on the information given in the previous question (question #1) and the call option price you just calculated, estimate the implied volatility of XYZ Corp stock?