# Assignment 2

Question 1:

1. The return of risk-free asset = \$1.10

U = 1.2 while d = 0.9

The risk-neutral probability governing the stock price movement will be;

=

=

=

1. The stock price (Sn) = 100

The strike price (K) = 100

The probabilities resulted will be u= 0.684 and d = 0.314

Obtaining the price of call= Max (Sn-K,0)

Obtaining price of put = Max (K-Sn,0)

The delta of the call will be;

=

=

=

1. The delta of the put

= d(call) – d(put) = 1

This will be the delta of the call less 1

= 1/3 – 1

1. Difference between the call delta and the put delta will be

The fact that the call has a positive delta while the put delta is a negative value show that this is a long call and a long put.

It means that if one had a call option, the value would decrease by -66.67% (-2/3 delta value) to convert into a put option but converting from a put option to a call option, the change would increase by 33.33% (1/3 delta value)

Question 2:

This may not be the case. When we assume a payoff diagram with the exercise prices of \$95 to \$100 call bull spread, near the \$95 stock price mark, it will look similar to a long call (convex curve). As volatility increases, the spread reacts positively but as it moves towards the \$100 stock price, the convexity curve changes and becomes negatively shaped like a short option position. It shows that it reacts negatively as volatility increases[ CITATION Sin10 l 7177 ]. It qualifies the statement that at-the-money options react to volatility than those that are further from the money. The 95 strike option we are long is sensitive more than the 100 strike option we are short.

## Works Cited

Sinclair, Euan. Option Trading: Pricing and Volatility Strategies and Techniques. New Jersey: John Wiley & Sons Inc, 2010.