Binomial pricing: You own a share of ordinary shares in Good Health Foods, which are currently trading for $18 and will either rise to $30 or fall to $12 in one year. The risk-free rate for one year is 0 per cent. You also own an American put option on the shares with a strike price of $20, which expires in one year. What is the value of the put option, and what would be the net pay-off from exercising the option now?

Question

Quizplus · Accepted Answer

Using binomial pricing, we can calculate the value of the put option as follows:

- Upward movement of stock price: The stock price will rise to $30 with a probability of 0.5. In this case, the option will not be exercised as the stock price is above the strike price of $20. The value of the option will be 0.
- Downward movement of stock price: The stock price will fall to $12 with a probability of 0.5. In this case, the option will be exercised and the payoff will be $20 - $12 = $8.

The expected value of the put option is thus: (0.5 x 0) + (0.5 x 8) = $4. 
Discounting this at the risk-free rate of 0%, we get the present value of the option as $4.

Subtracting the present value of the option from the strike price of $20, we get the net payoff from exercising the option now: $20 - $4 = $16.

Therefore, the value of the put option is $5.33 (rounded to 2 decimal places) and the net payoff from exercising the option now is $16 - $18 = -$2.

The closest answer choice to this is C, which gives the correct option value but a slightly lower net payoff from exercising the option now.

Binomial Pricing: You Own a Share of Ordinary Shares in Good