The Jacobi stochastic volatility model
Copyright policy )The Jacobi stochastic volatility model
We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the joint density of any finite sequence of log returns admits a Gram-Charlier A expansion with closed-form coefficients. We derive closed-form series representations for option prices whose discounted payoffs are functions of the asset price trajectory at finitely many time points. This includes European call, put, and digital options, forward start options, and can be applied to discretely monitored Asian options. In a numerical analysis we show that option prices can be accurately and efficiently approximated by truncating their series representations.
32 pages, 5 Figures, 1 Table
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [QFIN.PR]Quantitative Finance [q-fin]/Pricing of Securities [q-fin.PR], 330, polynomial model, Applications of stochastic analysis (to PDEs, etc.), Computational Finance (q-fin.CP), [QFIN.PR] Quantitative Finance [q-fin]/Pricing of Securities [q-fin.PR], [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], 510, FOS: Economics and business, Quantitative Finance - Computational Finance, Derivative securities (option pricing, hedging, etc.), stochastic volatility, JEL: C - Mathematical and Quantitative Methods/C.C3 - Multiple or Simultaneous Equation Models • Multiple Variables/C.C3.C32 - Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models • Diffusion Processes • State Space Models, option pricing, Numerical methods (including Monte Carlo methods), [QFIN.CP] Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], 91B25, 91B70, 91G20, 91G60, JEL: G - Financial Economics/G.G1 - General Financial Markets/G.G1.G13 - Contingent Pricing • Futures Pricing, Mathematics Subject Classification (2010): 91B25 91B70 91G20 91G60, Mathematical Finance (q-fin.MF), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Jacobi process, Quantitative Finance - Mathematical Finance, JEL: G - Financial Economics/G.G1 - General Financial Markets/G.G1.G12 - Asset Pricing • Trading Volume • Bond Interest Rates
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [QFIN.PR]Quantitative Finance [q-fin]/Pricing of Securities [q-fin.PR], 330, polynomial model, Applications of stochastic analysis (to PDEs, etc.), Computational Finance (q-fin.CP), [QFIN.PR] Quantitative Finance [q-fin]/Pricing of Securities [q-fin.PR], [QFIN.CP]Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], 510, FOS: Economics and business, Quantitative Finance - Computational Finance, Derivative securities (option pricing, hedging, etc.), stochastic volatility, JEL: C - Mathematical and Quantitative Methods/C.C3 - Multiple or Simultaneous Equation Models • Multiple Variables/C.C3.C32 - Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models • Diffusion Processes • State Space Models, option pricing, Numerical methods (including Monte Carlo methods), [QFIN.CP] Quantitative Finance [q-fin]/Computational Finance [q-fin.CP], 91B25, 91B70, 91G20, 91G60, JEL: G - Financial Economics/G.G1 - General Financial Markets/G.G1.G13 - Contingent Pricing • Futures Pricing, Mathematics Subject Classification (2010): 91B25 91B70 91G20 91G60, Mathematical Finance (q-fin.MF), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Jacobi process, Quantitative Finance - Mathematical Finance, JEL: G - Financial Economics/G.G1 - General Financial Markets/G.G1.G12 - Asset Pricing • Trading Volume • Bond Interest Rates
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