Question
In: Finance
Assume we have the following information for the call option written on CCC stock. Current price...
Assume we have the following information for the call option written on CCC stock. Current price of CCC stock is $160. Continuously compounded risk-free rate is 4%. Exercise price of the call option is $165, time to maturity is six months and the volatility of the BBB stock is 25%. Assume also that the continuously compounded dividend yield is 2.1%. i. Find the (theoretical) value of the call option using BSM valuation model. ii. Note that the only difference between company BBB and CCC is the dividend payment of CCC. Compare the call options prices of both and what is your conclusion about the effect of dividend on call option price?
Solutions
Expert Solution
Black and Scholes model of option valuation without dividend
Black and Scholes model of option valuation with dividend
| Input Data | CCC | BBB | |
| Stock Price now (S)- | 160 | 160 | |
| Exercise Price of Option (K) | 165 | 165 | |
| Compounded Dividend yield Rate (q) | 2.10% | 0 | |
| Number of periods to Exercise in years (t) | 0.50 | 0.50 | |
| Compounded Risk-Free Interest Rate (rf) | 4.00% | 4.00% | |
| Standard Deviation (annualized s) | 25.00% | 25.00% | |
| Output Data | CCC | BBB | |
| Present Value of Exercise Price (PV(K)) | 163.4399 | 161.733 | |
| s*t^.5 | 0.1768 | 0.177 | |
| d1 | -0.0319 | 0.027 | |
| d2 | -0.2087 | -0.149 | |
| Delta N(d1) Normal Cumulative Density Function | 0.4873 | 0.511 | |
| N(d2)*PV(K) | 68.2090 | 71.268 | |
| Value of Call | 8.9381 | 10.485 | |
Dividend yield has inverse relation with call price , i.e Call Price reduces with increase of dividend yield of shares
jeff jeffy answered 1 year agoRelated Solutions
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