The price of Ervin Corp. stock will either be $64 or $82 at the end of the year. Call options are available with one year until expiration. Continuously compounded T-bills currently yield 3.43 %. Suppose the current price of Ervin stock is $75.
What is the value of the call option if the strike price is $55 per share?
| Upmove (U)= High price/current price=82/75=1.0933 | ||||||
| Down move (D)= Low price/current price=64/75=0.8533 | ||||||
| Risk neutral probability for up move | ||||||
| q = (e^(risk free rate*time)-D)/(U-D) | ||||||
| =(e^(0.0343*1)-0.8533)/(1.0933-0.8533)=0.75651 | ||||||
| Call option payoff at high price (payoff H) | ||||||
| =Max(High price-strike price,0) | ||||||
| =Max(82-55,0) | ||||||
| =Max(27,0) | ||||||
| =27 | ||||||
| Call option payoff at low price (Payoff L) | ||||||
| =Max(Low price-strike price,0) | ||||||
| =Max(64-55,0) | ||||||
| =Max(9,0) | ||||||
| =9 | ||||||
| Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L) | ||||||
| =e^(-0.0343*1)*(0.756507*27+(1-0.756507)*9) | ||||||
| =21.85 |
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