Related papers: A Note on Delta Hedging in Markets with Jumps
Suppose an investor aims at Delta hedging a European contingent claim $h(S(T))$ in a jump-diffusion model, but incorrectly specifies the stock price's volatility and jump sensitivity, so that any hedging strategy is calculated under a…
Delta hedging, which plays a crucial r\^ole in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of…
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading of the underlying asset does not affect the price of that asset. This assumption can be fulfilled only in perfectly liquid markets.…
It is shown that delta hedging provides the optimal trading strategy in terms of minimal required initial capital to replicate a given terminal payoff in a continuous-time Markovian context. This holds true in market models where no…
We propose a model for hedging in a market with jumps for a large investor. The dynamics of the stock prices and the value process is governed by forward-backward SDEs driven by Teugels martingales. Unlike known FBSDE market models, ours…
We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal…
We consider option hedging in a model where the underlying follows an exponential L\'evy process. We derive approximations to the variance-optimal and to some suboptimal strategies as well as to their mean squared hedging errors. The…
We consider the performance of non-optimal hedging strategies in exponential L\'evy models. Given that both the payoff of the contingent claim and the hedging strategy admit suitable integral representations, we use the Laplace transform…
In the theory of riskfree hedges in continuous time finance, one can start with the delta-hedge and derive the option pricing equation, or one can start with the replicating, self-financing hedging strategy and derive both the delta-hedge…
We consider the jump-diffusion risky asset model and study its conditional prediction laws. Next, we explain the conditional least square hedging strategy and calculate its closed form for the jump-diffusion model, considering the…
In this work, we consider the hedging error due to discrete trading in models with jumps. Extending an approach developed by Fukasawa [In Stochastic Analysis with Financial Applications (2011) 331-346 Birkh\"{a}user/Springer Basel AG] for…
Explicit robust hedging strategies for convex or concave payoffs under a continuous semimartingale model with uncertainty and small transaction costs are constructed. In an asymptotic sense, the upper and lower bounds of the cumulative…
We introduce a new method of delta hedging. In many cases, this method results in a lower cost than the Black-Scholes method. To calculate the cost of hedging, we develop a Mathematica program that include the two-dimensional Newton-Raphson…
Options are contingent claims regarding the value of underlying assets. The Black-Scholes formula provides a road map for pricing these options in a risk-neutral setting, justified by a delta hedging argument in which countervailing…
This study deals with the problem of pricing European currency options in discrete time setting, whose prices follow the fractional Black Scholes model with transaction costs. Both the pricing formula and the fractional partial differential…
This study contributes to understanding Valuation Adjustments (xVA) by focussing on the dynamic hedging of Credit Valuation Adjustment (CVA), corresponding Profit & Loss (P&L) and the P&L explain. This is done in a Monte Carlo simulation…
We present here a regress later based Monte Carlo approach that uses neural networks for pricing high-dimensional contingent claims. The choice of specific architecture of the neural networks used in the proposed algorithm provides for…
We train neural networks to learn optimal replication strategies for an option when two replicating instruments are available, namely the underlying and a hedging option. If the price of the hedging option matches that of the Black--Scholes…
The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study…