Answer to Question #291287 in Financial Math for Hussy

Question

A speculator purchases a put option on British Pounds for 0.05$ per unit; the strike price is 1.50$.

A pound option represents 31.250 units

Assume that at the time of the purchase, the spot rate of the pound is 151$ and continually rises to 1.62$ by the expiration date.

1. Compute the highest net profit possible for the speculator based on the information above?

2. Compute the highest profit/loss for the seller of this put option?

Answer 1

A put option (or "put") is a contract that grants the option buyer the right, but not the responsibility, to sell (or sell short) a certain quantity of an underlying securities at a predetermined price within a predetermined time period. The striking price is the predetermined price at which the buyer of the put option can sell the underlying security. Put options are traded on a wide range of underlying assets, such as stocks, currencies, bonds, commodities, futures, and indices. A put option differs from a call option in that the holder has the right to buy the underlying securities at a defined price on or before the option contract's expiration date.

When investors are anxious that the stock market may collapse, they may purchase put options. That's because a put, which offers the right to sell an underlying asset at a certain price over a given period of time, often gains value as the underlying asset's price falls.

(A)

Payoff of put option:

=MaxKST,0

K=Strike price=1.5

ST=Value of underlying at expiration=1.62

Therefore, 

 option payoff=[Max1.5-1.62,0]=0

Cost of Put option=0.05 Per unit×31.250 units=1.5625

Loss of speculator=Cost-Payoff=1.5625-0=1.5625

(B)

Options being a zero sum same, the loss of speculator is gain of option seller.

Therefore, profit of option seller=1.5625