Question

1. You are asked to price options on KYC stock. KYC’s stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. KYC does not pay dividend. The risk free rate is 5% (EAR), and the current stock price of KYC is $100.

1. Price a European put option on KYC with maturity of 2 years and a strike price of 100.
2. Given the price of the put option that you calculated in a), specify the ranges of KYC share price at the option’s maturity date for which you will be making a net profit.
3. What is the price of the Call option at the same strike price?
4. Suppose you expect the price of KYC stock to have little variance in the future. How would you design a strategy (using options) to take advantage of this? Show your strategy explicitly. What are the payoffs of your strategy? What is the range in which you will make profits?

Answer 1

Ans(a). Uploaded through Photo.

Ans(b). For given time ,t=2 years

The option will be in the money for any price ranging between $0 and $100 for S , Say K=$100

Moreover, initially at t=0 the sum paid was $2.76. Hence, the profits share will range between $0 and $97.24

Mathematically, it's nothing but : $100-$2.76= $97.24

Therefore, after two years the initial which we paid ($2.76) will have worth around 2.76 x (1.05)2=$3.04.

Ans(c). Uploaded through Photo.

Ans(d): We can the Spreaded Butterfly Strategy in order to take advantage of this as we can assume that the price of the asset will not going to change majorly and will remain constant.

A long butterfly spread with calls is a three-section methodology that is made by getting one call at a lower strike value, selling two calls with a higher strike cost and getting one call with a significantly higher strike cost.The maximum profit is equivalent to the distinction between the least and center strike costs less the net expense of the position including commissions, and this benefit is acknowledged whether the stock cost is equivalent to the strike cost of the short calls (focus strike) at termination