Question

5. Option pricing - Single-period binomial approach

The value of an option can be calculated by using a step-by-step approach in the case of single periods or by using sophisticated formulas that can be easily created through a spreadsheet. In the real world, two possible outcomes for a stock price in six months is an assumption. The stock markets are volatile, and stocks move up and down based on market- and firm-specific factors.

Consider the case of SolarSystems Inc.:

Shares of SolarSystems Inc., a manufacturer of solar panels, sells for $40.00. Existing options allow for the option holder to purchase one additional share at an exercise price of $30.00. (Assume that you get the option for free!) The option will expire within one year. We can assume that at that time there will be a 70% chance that SolarSystems Inc.’s shares will sell for $56.00 and a 30% chance that the shares will be selling at $28.00.

Using the steps to the binomial approach, determine the following:

The expected end-term share price and return on SolarSystems Inc. shares are:     .

Based on the binomial approach, the range of payoff values at expiration for SolarSystems Inc.’s shares and options is:

$25.00 (share) and $20.00 (option)

$18.00 (share) and $15.00 (option)

$20.00 (share) and $30.00 (option)

$28.00 (share) and $26.00 (option)

Given this information, it is possible to create a riskless portfolio by selling one option and purchasing   shares.

Assuming that the risk–free rate is 8% and is compounded daily, current option price (VCVC) of the call option is   .

Answer 1

Page 20 Inswer Given details Current price of shore = $ 40 strike price = $30 St= 56 and s- - 28 ... Thus call is in the money by (56-30) = 26 and share has a payoff of ( 56 x 0.4+03x283122 = (39,2 +814)/2 = 47.612 = 23.8 nearly equals to fowith option. Hedge ratio = change in call price change in share price ( 26-0) on = 0.9286) ( 56-28) Riskless portfolio can be created by selling one option and purchasing 0.9286 Shares Call price = (0.+x26+0) /€20.08) 18.2/1.083287 $16.80