Question

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 theyemploy Black-Scholes model to estimate the implied volatility. Based on the information given in the previous questions (question #1 and #2) and the call option price you just calculated, estimate the implied volatility of XYZ Corp stock.

Question 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 calloption on XYZ Corp with the strike price of $105. (Attention: using a wrong approach will cost you all the credits)

Question 2. 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-free portfolio approach to price the 1-yearput option on XYZ Corp with the strike price of $105.

Answer 1

1. calculation of call option : Buy call option means Right to buy the Stock at exercise Price at future date by paying Premium to the writer of the Call Option.

Given Information ,

Spot price = $100

Rf(Risk free rate)= 5%

---Present Value = 1/(1+Rf) = 1/(1+.05)

Strike price = 105

#Maximum Value of call option Value = Spot Price

= $100

#Minimum value of Call option Value = Spot Price - present Value of Strike price

= $100- $105*(1/1.05)

= $100-$100

= $0

2. Put Optionn : Buy Put option means Right to Sell the Stock at exercise Price at future date by paying Premium to the writer of the Put Option

Given Information ,

Spot price = $100

Rf(Risk free rate)= 5%

---Present Value = 1/(1+Rf) = 1/(1+.05)

Strike price = 105

#Maximum Value of Put option = Present Value of Strike Price

= $105* (1/1.05)

= $100

#Minimum Value of Put Option = Present Value of Strike price - Spot Price

= $105*(1/1.05)-100

= $100-$100

= $0

Additional Information :

1.Call option ( right to Buy Stock at strike price )

*If Projected Stock price is $90 --- dont exercise the Option because the Market price on the date of Exercising the option (Projected Stock price)$90 is less than Exercise price $105

*If Projected Stock price is $120 --- exercise the Option because the Market price on the date of Exercising the option (Projected Stock price)$120 is more than Exercise pric $105   

2. For Put option ( right to Sell stock at Strike price )

*If Projected Stock price is $90 --- exercise the Option because the Market price on the date of Exercising the option (Projected Stock price)$90 is Less than Exercise price $105

i.e i sell @ $105 and buy the stock @90 so i can book gross profit of $15

*If Projected Stock price is $120 --- dont exercise the Option because the Market price on the date of Exercising the option (Projected Stock price)$120 is lmore than Exercise pric$105

{ i cancel the option and sell the share at market rate to others @ $120}