Variance optimal hedging for continuous time additive processes and applications

We consider variance-optimal hedging in general continuous-time affine stochastic volatility models. The optimal hedge and the associated hedging error are determined semiexplicitly in the case that the stock price follows a martingale. The integral representation of the solution opens the door to efficient numerical computation. The setup includes models with jumps in the stock price and in the activity process. It also allows for correlation between volatility and stock price movements. Concrete parametric models will be illustrated in a forthcoming paper.

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Variance-Optimal Hedging in General Affine Stochastic Volatility Models

Advances in Applied Probability ◽

10.1017/s000186780000392x ◽

2010 ◽

Vol 42 (01) ◽

pp. 83-105 ◽

Cited By ~ 1

Author(s):

Jan Kallsen ◽

Arnd Pauwels

Keyword(s):

Stochastic Volatility ◽

Continuous Time ◽

Stock Price ◽

Forthcoming Paper ◽

Parametric Models ◽

Stochastic Volatility Models ◽

Optimal Hedging ◽

Volatility Models ◽

Optimal Hedge ◽

General Affine

We consider variance-optimal hedging in general continuous-time affine stochastic volatility models. The optimal hedge and the associated hedging error are determined semiexplicitly in the case that the stock price follows a martingale. The integral representation of the solution opens the door to efficient numerical computation. The setup includes models with jumps in the stock price and in the activity process. It also allows for correlation between volatility and stock price movements. Concrete parametric models will be illustrated in a forthcoming paper.

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Continuous-time Markov additive processes: Composition of large deviations principles and comparison between exponential rates of convergence

Journal of Applied Probability ◽

10.1239/jap/1011994182 ◽

2001 ◽

Vol 38 (4) ◽

pp. 917-931 ◽

Cited By ~ 4

Author(s):

Claudio Macci

Keyword(s):

Large Deviations ◽

Continuous Time ◽

Fluid Model ◽

Variational Formula ◽

Rates Of Convergence ◽

Rate Function ◽

Large Deviations Principle ◽

Additive Process ◽

Additive Processes ◽

Markov Additive Processes

We consider a continuous-time Markov additive process (Jt,St) with (Jt) an irreducible Markov chain on E = {1,…,s}; it is known that (St/t) satisfies the large deviations principle as t → ∞. In this paper we present a variational formula H for the rate function κ∗ and, in some sense, we have a composition of two large deviations principles. Moreover, under suitable hypotheses, we can consider two other continuous-time Markov additive processes derived from (Jt,St): the averaged parameters model (Jt,St(A)) and the fluid model (Jt,St(F)). Then some results of convergence are presented and the variational formula H can be employed to show that, in some sense, the convergences for (Jt,St(A)) and (Jt,St(F)) are faster than the corresponding convergences for (Jt,St).

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Continuous-time Markov additive processes: Composition of large deviations principles and comparison between exponential rates of convergence

Journal of Applied Probability ◽

10.1017/s0021900200019136 ◽

2001 ◽

Vol 38 (04) ◽

pp. 917-931 ◽

Cited By ~ 1

Author(s):

Claudio Macci

Keyword(s):

Large Deviations ◽

Continuous Time ◽

Fluid Model ◽

Variational Formula ◽

Rates Of Convergence ◽

Rate Function ◽

Large Deviations Principle ◽

Additive Process ◽

Additive Processes ◽

Markov Additive Processes

We consider a continuous-time Markov additive process (J t ,S t ) with (J t ) an irreducible Markov chain on E = {1,…,s}; it is known that (S t /t) satisfies the large deviations principle as t → ∞. In this paper we present a variational formula H for the rate function κ∗ and, in some sense, we have a composition of two large deviations principles. Moreover, under suitable hypotheses, we can consider two other continuous-time Markov additive processes derived from (J t ,S t ): the averaged parameters model (J t ,S t (A)) and the fluid model (J t ,S t (F)). Then some results of convergence are presented and the variational formula H can be employed to show that, in some sense, the convergences for (J t ,S t (A)) and (J t ,S t (F)) are faster than the corresponding convergences for (J t ,S t ).

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Optimal Hedging in Discrete and Continuous Time

SSRN Electronic Journal ◽

10.2139/ssrn.1522090 ◽

2009 ◽

Cited By ~ 10

Author(s):

Bruno Remillard ◽

Sylvain Rubenthaler

Keyword(s):

Continuous Time ◽

Optimal Hedging

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Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

Journal of Applied Probability ◽

10.1017/s0021900200002965 ◽

2007 ◽

Vol 44 (02) ◽

pp. 285-294 ◽

Cited By ~ 2

Author(s):

Qihe Tang

Keyword(s):

Asymptotic Formula ◽

Continuous Time ◽

Heavy Tails ◽

Tail Behavior ◽

Renewal Model ◽

Discounted Aggregate Claims ◽

Aggregate Claims ◽

Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

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