The double Heston model via filtering methods

Namundjebo, Elia N (2016-12)

Thesis (MSc)--Stellenbosch University, 2016

Thesis

ENGLISH ABSTRACT : Stochastic volatility models are well-known for their ability to generate a volatility smile for financial securities. The development of the stochastic volatility models followed shortly after the crash of 1987 which violates the Black-Scholes model which has constant volatility. In this study we introduce non-linear filtering methods to estimate the implied volatilities of the Double Heston model. We compare our results to the Standard Heston model. The non-linear filtering methods used are the extended Kalman filter, the unscented Kalman filter and the particle filter. We combine the filtering methods together with the maximum likelihood estimation method to estimate the model's hidden parameters. Our numerical results show that the Double Heston model ts the market implied volatilities better than the Standard Heston model. The particle lter also performs better than the other two filters.

AFRIKAANSE OPSOMMING : Stogastiese wisselvalligheid modelle is goed bekend vir hul vermoë om'n wisselvalligheid glimlag vir finansiële sekuriteite te genereer. Die ontwikkeling van die stogastiese wisselvalligheid modelle het gevolg kort nadat die ongeluk van 1987 wat die Black-Scholes model wat konstant wisselvalligheid oortree het. In hierdie studie stel ons nie-lineêre filter metodes voor om die ge lmpliseerde wisselings in die Double Heston Model te skat. Ons vergelyk ons resultate aan die Standard Heston model. Die nie-lineêre lter metodes wat gebruik word is die uitgebreide Kalman filter, die reuklose Kalman filter en die deeltjies fillter. Ons kombineer die filter metodes saam met die maksimum annneemlikheidsberaming metode om verborge parameters van die model te skat. Ons numeriese resultate dui daarop dat die Double Heston model pas die mark geïmpliseerde volatiliteit en beter as die Standard Heston model. Die deeltjie filter presteer ook beter as die ander twee fillters.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/100371
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