Mathematics of parallel stratagems
Parallel stratagems are used as hedging strategies by investors to minimise their exposure to risk in the financial markets. Options are one of the most popularly used instruments for effective hedging. A number of mathematical models have been developed for predicting the price of option cont...
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Format: | Final Year Project |
Language: | English |
Published: |
2017
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Online Access: | http://hdl.handle.net/10356/71695 |
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Institution: | Nanyang Technological University |
Language: | English |
Summary: | Parallel stratagems are used as hedging strategies by investors to minimise their
exposure to risk in the financial markets. Options are one of the most popularly used
instruments for effective hedging. A number of mathematical models have been
developed for predicting the price of option contracts that enable investors to optimally
hedging their portfolios.
Three of the most widely used models are the Black-Scholes for pricing European
options, Binomial Tree for pricing American options and Monte Carlo Simulations for
pricing Asian options. All of them are built on fundamental financial theories like the
no-arbitrage principle, efficient market hypothesis and risk-neutral measures. However,
these theories are not completely realistic and showcase certain discrepancies from the
real world behaviour of financial markets. This is one of the root causes for the
inaccuracies in the model‟s predictions.
The empirical tests of the Black-Scholes model indicate that though it is fairly accurate
in pricing all European options, the model performs best in short-time horizons and at
times of low market volatility. Moreover, the model is not well-suited for pricing
American and Asian options as it gives unfavourable results when compared with the
other two models of Binomial Tree and Monte Carlo. In addition to that, critical
evaluation of the model highlights a major mathematical error in its derivation that
renders it logically incoherent.
This report aims to correct that mathematical error and in general, proposes plausible
modifications or extensions to the existing Black-Scholes model so as to make it
empirically stronger as well as suitable for pricing options of styles other than European.
ii
The report makes three proposals out of which two (Proposals 1 and 3) are deemed to be
successful as they are supported by logical reasoning and generate favourable results.
Proposal 1 corrects the model‟s mathematical error by assuming that the time-integrated
value of an option‟s delta is a constant, and Proposal 3 aims to make the model a better
fit for pricing Asian options by minimising the fluctuations in the value of a delta
hedged portfolio throughout its lifetime. |
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