Pemodelan Nilai Opsi Tipe Eropa

Abstract

Option is the right to sell or buy a specified quantity of some underlying asset by paying a specified exercise price, on or before an expiration date. There are two basic types of options, calls and puts. A call option is the right to buy and a put option is the right to sell the underlying asset. There are two types of options according to its execution time, i.e. American and European options. American options can be exercised at any time the holder wishes until the expiration date, while European options can only be exercised on the expiration date. Modelling of option price usually is done analytically by determining solution of differential equation that is satisfied by the price of derivative asset, known as Black-Scholes equation. Because option price is a reflection of present value of expectation of difference between the exercise price and the stock price at expiration date, so it is necessary to study the option price through the concept of present value, as an alternative way to model the option price. The result of this study shows that modelling of option price using differential equation method and present value approach give the same option price. Furthermore the results of ilustration give informations about the relation of the option price with its parameters as follow: First, increase in the current stock price causes the call option price also to increase, while the put option price, on the contrary, will decrease. Second, increase in the exercise price causes the call option price to decrease, while the put option price will increase. Third, the longer the expiration time the call option price will be higher, while the put option price doesn’t have the same tendency, but it depends on other parameters. Fourth, increase in the interest rate causes the call option price to increase, while the put option price will decrease. Finally, increase in the volatility causes the price of both call option and put option will increase.