Pricing options on realized variance in the Heston model with jumps in returns and volatility Part II. An approximate distribution of discrete variance

2012 ◽  
Vol 16 (2) ◽  
pp. 3-32 ◽  
Author(s):  
Artur Sepp
Keyword(s):  
Heston Model ◽  
Realized Variance ◽  
Pricing Options ◽  
Approximate Distribution

Pricing Options on Realized Variance

2005 ◽  
Author(s):  
Peter P. Carr ◽  
Hélyette Geman ◽  
Dilip B. Madan ◽  
Marc Yor
Keyword(s):  
Realized Variance ◽  
Pricing Options

Pricing options on realized variance

2005 ◽  
Vol 9 (4) ◽  
pp. 453-475 ◽  
Author(s):  
Peter Carr ◽  
Hélyette Geman ◽  
Dilip B. Madan ◽  
Marc Yor
Keyword(s):  
Realized Variance ◽  
Pricing Options

scholarly journals FAST HILBERT TRANSFORM ALGORITHMS FOR PRICING DISCRETE TIMER OPTIONS UNDER STOCHASTIC VOLATILITY MODELS

2015 ◽  
Vol 18 (07) ◽  
pp. 1550046 ◽  
Author(s):  
PINGPING ZENG ◽  
YUE KUEN KWOK ◽  
WENDONG ZHENG
Keyword(s):  
Stochastic Volatility ◽  
Hilbert Transform ◽  
Asset Price ◽  
Heston Model ◽  
Expiration Date ◽  
Realized Variance ◽  
Stochastic Volatility Models ◽  
Underlying Asset ◽  
Volatility Models ◽  
Volatility Model

Timer options are barrier style options in the volatility space. A typical timer option is similar to its European vanilla counterpart, except with uncertain expiration date. The finite-maturity timer option expires either when the accumulated realized variance of the underlying asset has reached a pre-specified level or on the mandated expiration date, whichever comes earlier. The challenge in the pricing procedure is the incorporation of the barrier feature in terms of the accumulated realized variance instead of the usual knock-out feature of hitting a barrier by the underlying asset price. We construct the fast Hilbert transform algorithms for pricing finite-maturity discrete timer options under different types of stochastic volatility processes. The stochastic volatility processes nest some popular stochastic volatility models, like the Heston model and 3/2 stochastic volatility model. The barrier feature associated with the accumulated realized variance can be incorporated effectively into the fast Hilbert transform procedure with the computational convenience of avoiding the nuisance of recovering the option values in the real domain at each monitoring time instant in order to check for the expiry condition. Our numerical tests demonstrate high level of accuracy of the fast Hilbert transform algorithms. We also explore the pricing properties of the timer options with respect to various parameters, like the volatility of variance, correlation coefficient between the asset price process and instantaneous variance process, sampling frequency, and variance budget.

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