By comparing the different continuous interest rate of the European long call price, when the strike price increases, the long call spread will increase to the peak point and then decrease. In special, when the present price is equal to the discounted strike price, the long call spread reaches to the peak point. There is negative relationship between option price and the riskless continuous interest rates. By comparing the different number of revision times of the European long call price, with fixed riskless continuous interest rate, when the number of revision times increase, the option price will slightly increase. With the fixed number of revision time, when the riskless continuous interest rate increases, the option price will significantly increase. By comparing the different standard deviation of the European long call price, with fixed transaction cost rate on stocks, when the number of revision time increases, the option price will slightly decrease. Moreover, there is positive relationship between the volatility of the risky asset (standard deviation) and option price.
By comparing the European short call price, the transaction cost rate on stocks k can negatively affect the option price. Moreover, there is negative relationship between option price and the riskless continuous interest rates. There is significant difference between the option price without transaction costs and the option price with transaction costs. Both the Black Scholes approximation and Leland’s approximation can get accurate value of option price. On the other hand, when there are transaction costs, there is no significant difference between the Black Scholes approximation and the Leland’s approximation.
