VALUATION, HEDGING, AND BOUNDS OF SWAPS UNDER MULTI-FACTOR BNS-TYPE STOCHASTIC VOLATILITY MODELS

In this paper, we consider price weighted-volatility swap and price weighted-variance swap. The underlying asset considered in this paper is assumed to follow a general stochastic differential equation and exhibits stochastic volatility. We obtain analytical pricing formulas for the weighted-variance swap and approximate expression for the weighted-volatility swap. Nice bounds for the arbitrage-free variance swap price are also found. The proposed pricing formulas are easy to implement in real time and can be applied efficiently for practical applications. We consider the problem of hedging volatility swap with variance swap and obtain analytical formula for the hedge ratio. We also consider a problem of hedging an asset with variance swap and option. We determined the optimal amount of the underlying asset that has to be held for minimizing the hedging error by taking positions in options and weighted-variance swap. A numerical example is also provided.

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A Stochastic Volatility Alternative to SABR

Journal of Applied Probability ◽

10.1017/s0021900200004988 ◽

2008 ◽

Vol 45 (04) ◽

pp. 1071-1085

Author(s):

L. C. G. Rogers ◽

L. A. M. Veraart

Keyword(s):

Brownian Motion ◽

Stochastic Processes ◽

Closed Form ◽

Stochastic Volatility ◽

Option Prices ◽

Stochastic Volatility Models ◽

Underlying Asset ◽

Volatility Models ◽

Sabr Model ◽

Modified Dynamics

We present two new stochastic volatility models in which option prices for European plain-vanilla options have closed-form expressions. The models are motivated by the well-known SABR model, but use modified dynamics of the underlying asset. The asset process is modelled as a product of functions of two independent stochastic processes: a Cox-Ingersoll-Ross process and a geometric Brownian motion. An application of the models to options written on foreign currencies is studied.

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Local, Stochastic Volatility Models, Static Hedging and Variance Swap

Financial Mathematics, Derivatives and Structured Products ◽

10.1007/978-981-13-3696-6_19 ◽

2019 ◽

pp. 233-247

Author(s):

Raymond H. Chan ◽

Yves ZY. Guo ◽

Spike T. Lee ◽

Xun Li

Keyword(s):

Stochastic Volatility ◽

Stochastic Volatility Models ◽

Variance Swap ◽

Static Hedging ◽

Volatility Models

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

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024915500466 ◽

2015 ◽

Vol 18 (07) ◽

pp. 1550046 ◽

Cited By ~ 3

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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