Related papers: Robustness of Delta Hedging in a Jump-Diffusion Mo…
Modelling stock prices via jump processes is common in financial markets. In practice, to hedge a contingent claim one typically uses the so-called delta-hedging strategy. This strategy stems from the Black--Merton--Scholes model where it…
We price and replicate a variety of claims written on the log price $X$ and quadratic variation $[X]$ of a risky asset, modeled as a positive semimartingale, subject to stochastic volatility and jumps. The pricing and hedging formulas do…
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 a market with a rough or Markovian mean-reverting stochastic volatility there is no perfect hedge. Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets in the case of European options. A…
We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the market's important features. Assuming some mild condition on the jump size…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
In most real scenarios the construction of a risk-neutral portfolio must be performed in discrete time and with transaction costs. Two human imposed constraints are the risk-aversion and the profit maximization, which together define a…
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 study option pricing and hedging with uncertainty about a Black-Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this…
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…
The dynamic hedging theory only makes sense in the setup of one given model, whereas the practice of dynamic hedging is just the opposite, with models fleeing after the data through daily recalibration. This is quite of a quantitative…
This work focuses on the dynamic hedging of financial derivatives, where a reinforcement learning algorithm is designed to minimize the variance of the delta hedging process. In contrast to previous research in this area, we apply…
Optimal B-robust estimate is constructed for multidimensional parameter in drift coefficient of diffusion type process with small noise. Optimal mean-variance robust (optimal V -robust) trading strategy is find to hedge in mean-variance…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
Discrete time hedging in a complete diffusion market is considered. The hedge portfolio is rebalanced when the absolute difference between delta of the hedge portfolio and the derivative contract reaches a threshold level. The rate of…
The recent work of Horikawa and Nakagawa (2024) claims that under a complete market admitting statistical arbitrage, the difference between the hedging position provided by deep hedging and that of the replicating portfolio is a statistical…
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…
In financial mathematics, the calculation of the Greeks, especially the delta, is emphasized due to its role in risk management. In this article, we employ Malliavin calculus to determine the delta of European and Asian options, where the…
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…
This paper investigates the pricing of financial derivatives and the calculation of their delta Greek when the underlying asset is a jump-diffusion process in which the stochastic intensity component follows the CIR process. Utilizing…