Monte Carlo Simulation Valuation of American Basket Options
Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
Background - Pricing American options with long time to maturity could be challenging since the holder of the option has the right to exercise it at any time point before the maturity. There are a number of studies carried out on pricing this type of options and numerous algorithms as well as several techniques have been developed in order to optimize and enhance the accuracy of the pricing procedure. Monte Carlo simulation is a well-known method for option pricing in which paths are generated to calculate the payoffs that determine the value of the option. By employing Monte Carlo simulation, Longstaff and Schwartz (2001) presented the Least Squares approach for American options valuation. This approach is applicable to American options, including put basket options. We chose to utilize this model on account of its simplicity and adaptability for basket options.
Purpose – In this study, the main purpose is to value an American put basket option by making use of Least Squares Monte Carlo simulation. In other words, the current thesis aims at implementing the Monte Carlo regression-based approach. Furthermore, we intend to analyse the effects of changing main parameters on the value of the basket option. These parameters are strike, maturity, spot rate, risk-free rate and volatility.
Method - In order to implement Monte Carlo simulation, we decided to form a basket option consisting of ten foreign exchange rates, including US Dollar (USD), Euro (EUR), Japanese Yen (JPY), British Pound (GBP), Danish Krone (DKK), Czech Kruna (CZK), Norwegian Krone (NOK), Singapore Dollar (SGD), Canadian Dollar (CAD) and Korean Won (KRW). We considered the Swedish Krona (SEK) as the domestic currency. In addition, five-year government bonds are included as the risk-free rates. The data were collected from Datastream over a five-year period starting at 2011. Having done obtaining the data, through calculating correlation matrix and log returns for each exchange rate, the basket option was formed. After that, Least Squares Monte Carlo simulation was utilized for pricing American basket option. We used R as well as Excel to run the simulation and analyse the effects of changing the parameters.
Conclusion – In addition to using Excel for Monte Carlo Simulation and Least Squares model, we managed to implement the American option pricing in R. Regarding the impact of changes in parameters, increasing strike and time to maturity cause expected rise in the basket option value. On the other hand, if risk-free rate and spot rate climb up, the value would decline correspondently. Furthermore, results are consistent with the assumption that American options are valued at least as high as European options with the same characteristics.
Place, publisher, year, edition, pages
2016. , 52 p.
Option Pricing, American Basket Put Option, Least Squares Monte Carlo Simulation, Greeks
IdentifiersURN: urn:nbn:se:hj:diva-30438ISRN: JU-IHH-FÖA-2-20160249OAI: oai:DiVA.org:hj-30438DiVA: diva2:936002
Subject / course
IHH, Business Administration