5,739 research outputs found
Robustness of quadratic hedging strategies in finance via backward stochastic differential equations with jumps
We consider a backward stochastic differential equation with jumps (BSDEJ)
which is driven by a Brownian motion and a Poisson random measure. We present
two candidate-approximations to this BSDEJ and we prove that the solution of
each candidate- approximation converges to the solution of the original BSDEJ
in a space which we specify. We use this result to investigate in further
detail the consequences of the choice of the model to (partial) hedging in
incomplete markets in finance. As an application, we consider models in which
the small variations in the price dynamics are modeled with a Poisson random
measure with infinite activity and models in which these small variations are
modeled with a Brownian motion. Using the convergence results on BSDEJs, we
show that quadratic hedging strategies are robust towards the choice of the
model and we derive an estimation of the model risk
Robustness of quadratic hedging strategies in finance via Fourier transforms
In this paper we investigate the consequences of the choice of the model to partial hedging in incomplete markets in finance. In fact we consider two models for the stock price process. The first model is a geometric Lévy process in which the small jumps might have infinite activity. The second model is a geometric Lévy process where the small jumps are truncated or replaced by a Brownian motion which is appropriately scaled. To prove the robustness of the quadratic hedging strategies we use pricing and hedging formulas based on Fourier transform techniques. We compute convergence rates and motivate the applicability of our results with examples
Robust Hedging of Variance Swaps: Discrete Sampling & Co-maturing European Options
In the practice of quantitative finance, model risk has raised significant concern and thus model-independent hedging is of particular interest to both academia and industry. In this thesis, we review two methods of constructing robust and model-independent hedging portfolios of variance swaps. One of them assumes a continuum of European options trade but does not require the underlying asset's price path to be continuous. However, the other assumes finite number of options quoted but requires the continuity of underlying asset's price path. We explore numerically the hedging performance as well as upper and lower bounds of several numerical examples by implementing these two methods. Finally, we try to combine these two methods and use an example to show an idea of a possible approach of doing this
Hedging strategies and minimal variance portfolios for European and exotic options in a Levy market
This paper presents hedging strategies for European and exotic options in a
Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con-
structed under different market assumptions, such as the existence of power
jump assets or moment swaps. In the case of European options or baskets of
European options, static hedging is implemented. It is shown that perfect
hedging can be achieved. Delta and gamma hedging strategies are extended to
higher moment hedging by investing in other traded derivatives depending on the
same underlying asset. This development is of practical importance as such
other derivatives might be readily available. Moment swaps or power jump assets
are not typically liquidly traded. It is shown how minimal variance portfolios
can be used to hedge the higher order terms in a Taylor expansion of the
pricing function, investing only in a risk-free bank account, the underlying
asset and potentially variance swaps. The numerical algorithms and performance
of the hedging strategies are presented, showing the practical utility of the
derived results.Comment: 32 pages, 6 figure
Asymptotic Power Utility-Based Pricing and Hedging
Kramkov and Sirbu (2006, 2007) have shown that first-order approximations of
power utility-based prices and hedging strategies can be computed by solving a
mean-variance hedging problem under a specific equivalent martingale measure
and relative to a suitable numeraire. In order to avoid the introduction of an
additional state variable necessitated by the change of numeraire, we propose
an alternative representation in terms of the original numeraire. More
specifically, we characterize the relevant quantities using semimartingale
characteristics similarly as in Cerny and Kallsen (2007) for mean-variance
hedging. These results are illustrated by applying them to exponential L\'evy
processes and stochastic volatility models of Barndorff-Nielsen and Shephard
type.Comment: 32 pages, 4 figures, to appear in "Mathematics and Financial
Economics
Jump starting GARCH: pricing and hedging options with jumps in returns and volatilities
This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan’s GARCH option models, where conditional returns are constrained to being normal, as well as mixed jump processes as used in Merton. The diffusion limits of our model have been shown to include jump diffusion models, stochastic volatility models and models with both jumps and diffusive elements in both returns and volatilities. Empirical analysis on the S&P 500 index reveals that the incorporation of jumps in returns and volatilities adds significantly to the description of the time series process and improves option pricing performance. In addition, we provide the first-ever hedging effectiveness tests of GARCH option models.Options (Finance) ; Hedging (Finance)
Utility based pricing and hedging of jump diffusion processes with a view to applications
We discuss utility based pricing and hedging of jump diffusion processes with
emphasis on the practical applicability of the framework. We point out two
difficulties that seem to limit this applicability, namely drift dependence and
essential risk aversion independence. We suggest to solve these by a
re-interpretation of the framework. This leads to the notion of an implied
drift. We also present a heuristic derivation of the marginal indifference
price and the marginal optimal hedge that might be useful in numerical
computations.Comment: 23 pages, v2: publishe
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