| Summary: | 碩士 === 國立東華大學 === 企業管理學系 === 90 === Option pricing model is always a charming and worth learning subject. Implied probability distribution is one of the key topics in this field.
We use a risk-neutral valuation technique to construct pricing formula. Then we use the index option prices to estimate the parameters of a mixture of two lognomals in order to recover a settlement implied PDF (probability density function). We can set different type and amount of constraints. In this thesis, we estimate the implied distribution for LIFFE FTSE 100 option market as a mixture of two lognormals (hereafter, the M-T model), and then we compare it with the Black-Scholes model (hereafter, the B-S model).
We find that the implied probability distribution of index option prices is not always a lognormal but with leptokurtosis. Implied volatility of the B-S model is shown to be smirk-pattern .We also find that the M-T model is more flexible in interpreting index option prices than the B-S model.
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