Monte Carlo Simulation in Finance to Calculate European Options Value
Monte Carlo Simulation in Finance for Calculating European Options Value
1. Introduction
An option is a financial instrument whose value depends on a value of underlying security. Options trade started in 1973 at the Chicago Board Options Exchange (Hull, Fundamentals of futures and options markets 2008). Nowadays, options have become a crucial tool in finance; they have become valuable both for financial institutions and investors. Options are attractive to investors since they have great effect in reducing risk in investment. Throughout this independent study, we will be working within the European option. A European option is a vanilla option. A vanilla option is a standard type of option contract with no special features except the simple expiry date (the date in the contract) and the predetermined strike price (the agreed price at which a particular option price can be exercised). There are two types of European option; European call options and European put options. European call options give the owner the right, but not the obligation, to buy an agreed quantity of underlying securities on a certain time (the expiration date), for a specified price (the strike price). The expiration date is called the day until maturity. The seller of call options is obligated to sell the security should the buyer so decide. Vice versa, European put options give the owner the right, but not the obligation, to sell an agree quantity of an underlying securities on a certain time for a specified price. The seller of put options is obligated to buy the security if the buyer so decides. The buyer pays a fee (called premium) for both of these rights. For each call options or put options, there are three conditions; ITM (In-the-money), OTM (Out-of-the-money), and ATM (At-the-money). Call option is called ITM when the strike
price is below the current underlying security’s price (spot price). In this situation, the holder can get a gain (payoff). On the other hand, call option
1. Introduction
An option is a financial instrument whose value depends on a value of underlying security. Options trade started in 1973 at the Chicago Board Options Exchange (Hull, Fundamentals of futures and options markets 2008). Nowadays, options have become a crucial tool in finance; they have become valuable both for financial institutions and investors. Options are attractive to investors since they have great effect in reducing risk in investment. Throughout this independent study, we will be working within the European option. A European option is a vanilla option. A vanilla option is a standard type of option contract with no special features except the simple expiry date (the date in the contract) and the predetermined strike price (the agreed price at which a particular option price can be exercised). There are two types of European option; European call options and European put options. European call options give the owner the right, but not the obligation, to buy an agreed quantity of underlying securities on a certain time (the expiration date), for a specified price (the strike price). The expiration date is called the day until maturity. The seller of call options is obligated to sell the security should the buyer so decide. Vice versa, European put options give the owner the right, but not the obligation, to sell an agree quantity of an underlying securities on a certain time for a specified price. The seller of put options is obligated to buy the security if the buyer so decides. The buyer pays a fee (called premium) for both of these rights. For each call options or put options, there are three conditions; ITM (In-the-money), OTM (Out-of-the-money), and ATM (At-the-money). Call option is called ITM when the strike
price is below the current underlying security’s price (spot price). In this situation, the holder can get a gain (payoff). On the other hand, call option