Explain the concept of Put-Call Parity using both the formula and by plotting the payoffs as a function of the stock price.

b. Option traders often refer to straddles and butterflies. Straddle: buy call with exercise price of $100 and simultaneously by put with exercise price of $100. Butterfly: Simultaneously buy one call with exercise price of $100, sell two calls with exercise price of $110, and buy one call with exercise price of $120.

i. Draw position diagrams for the straddle and the butterfly, showing the payoffs from the investors net position.

ii. Each strategy is a bet on variability. Explain Briefly the nature of this bet.

c. A stocks current price is $160, and there are two possible prices that may occur next period: $150 or $175. The interest rate on risk-free investments is 6% per period. Assume that a (European) call option exists on this stock having an exercise price of $155.

i. How could you form a portfolio based on the stock and the call so as to achieve a risk-free hedge?

ii. Compute the price of the call. iii. What would change if the exercise price was $180?