Related papers: A Note on Delta Hedging in Markets with Jumps
In this paper we study the existence of an optimal hedging strategy for the shortfall risk measure in the game options setup. We consider the continuous time Black--Scholes (BS) model. Our first result says that in the case where the game…
Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate…
Utility based methods provide a very general theoretically consistent approach to pricing and hedging of securities in incomplete financial markets. Solving problems in the utility based framework typically involves dynamic programming,…
At first, we solve a problem of finding a risk-minimizing hedging strategy on a general market with ratings. Next, we find a solution to this problem on Markovian market with ratings on which prices are influenced by additional factors and…
Agent-based models help explain stock price dynamics as emergent phenomena driven by interacting investors. In this modeling tradition, investor behavior has typically been captured by two distinct mechanisms -- learning and heterogeneous…
We propose a hedging approach for general contingent claims when liquidity is a concern and trading is subject to transaction cost. Multiple assets with different liquidity levels are available for hedging. Our risk criterion targets a…
In an incomplete market setting, we consider two financial agents, who wish to price and trade a non-replicable contingent claim. Assuming that the agents are utility maximizers, we propose a transaction price which is a result of the…
We develop a robust framework for pricing and hedging of derivative securities in discrete-time financial markets. We consider markets with both dynamically and statically traded assets and make minimal measurability assumptions. We obtain…
The studied model was suggested to design a perfect hedging strategy for a large trader. In this case the implementation of a hedging strategy affects the price of the underlying security. The feedback-effect leads to a nonlinear version of…
This article presents a deep reinforcement learning approach to price and hedge financial derivatives. This approach extends the work of Guo and Zhu (2017) who recently introduced the equal risk pricing framework, where the price of a…
Prices of tradables can only be expressed relative to each other at any instant of time. This fundamental fact should therefore also hold for contigent claims, i.e. tradable instruments, whose prices depend on the prices of other tradables.…
We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance $n^{-1}$ between trading times. We derive a non…
We study shortfall risk minimization for American options with path dependent payoffs under proportional transaction costs in the Black--Scholes (BS) model. We show that for this case the shortfall risk is a limit of similar terms in an…
We describe the pricing and hedging of financial options without the use of probability using rough paths. By encoding the volatility of assets in an enhancement of the price trajectory, we give a pathwise presentation of the replication of…
Deep hedging uses recurrent neural networks to hedge financial products that cannot be fully hedged in incomplete markets. Previous work in this area focuses on minimizing some measure of quadratic hedging error by calculating pathwise…
We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uniformly ergodic jump Markov process with a countable state…
We study a notion of good-deal hedging, that corresponds to good-deal valuation for generalized good-deal constraints. Under model uncertainty about the market prices of risk of hedging assets, a robust approach leads to a reduction or even…
We present an explicit hedging strategy, which enables to prove arbitrageness of market incorporating at least two assets depending on the same random factor. The implied Black-Scholes volatility, computed taking into account the form of…
We consider the valuation of contingent claims with delayed dynamics in a Black&Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how…
We consider the problem of optimal investment and consumption in a class of multidimensional jump-diffusion models in which asset prices are subject to mutually exciting jump processes. This captures a type of contagion where each downward…