Suppose VS's stock price is currently $20. In the next six months it will either fall to $10 or rise to $30. What is the current value of a put option with an exercise price of $15? The six-month risk-free interest rate is 5% (periodic rate).
Please indicate the formula
| Upmove (U)= High price/current price=30/20=1.5 | ||||||
| Down move (D)= Low price/current price=10/20=0.5 | ||||||
| Risk neutral probability for up move | ||||||
| q = (e^(risk free rate*time)-D)/(U-D) | ||||||
| =(e^(0.1*0.5)-0.5)/(1.5-0.5)=0.55127 | ||||||
| Put option payoff at high price (payoff H) | ||||||
| =Max(Strike price-High price,0) | ||||||
| =Max(15-30,0) | ||||||
| =Max(-15,0) | ||||||
| =0 | ||||||
| Put option payoff at low price (Payoff L) | ||||||
| =Max(Strike price-low price,0) | ||||||
| =Max(15-10,0) | ||||||
| =Max(5,0) | ||||||
| =5 | ||||||
| Price of Put option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L) | ||||||
| =e^(-0.1*0.5)*(0.551271*0+(1-0.551271)*5) | ||||||
| =2.13 |
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