Related papers: Volatility derivatives in market models with jumps
We present a general framework for the estimation of corporate default based on a firm's capital structure, when its assets are assumed to follow a pure jump L\'evy processes; this setup provides a natural extension to usual default metrics…
We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of…
Recognizing the importance of jump risk in option pricing, we propose a neural jump stochastic differential equation model in this paper, which integrates neural networks as parameter estimators in the conventional jump diffusion model. To…
This paper investigates the optimal choices of financial derivatives to complete a financial market in the framework of stochastic volatility (SV) models. We introduce an efficient and accurate simulation-based method, applicable to…
In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation…
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local…
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…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
This paper introduces a jump-diffusion pricing model specifically designed for algorithmic trading and high-frequency trading (HFT). The model incorporates independent jump and diffusion processes, providing a more precise representation of…
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…
This paper studies the problem of option replication in general stochastic volatility markets with transaction costs, using a new specification for the volatility adjustment in Leland's algorithm \cite{Leland}. We prove several limit…
In this paper we study the Fourier estimator of Malliavin and Mancino for the spot volatility. We establish the convergence of the trigonometric polynomial to the volatility's path in a setting that includes the following aspects. First,…
In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…
Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which…
Cryptocurrencies, especially Bitcoin (BTC), which comprise a new digital asset class, have drawn extraordinary worldwide attention. The characteristics of the cryptocurrency/BTC include a high level of speculation, extreme volatility and…
An appropriate calibration and forecasting of volatility and market risk are some of the main challenges faced by companies that have to manage the uncertainty inherent to their investments or funding operations such as banks, pension funds…
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…
We consider a method of lines (MOL) approach to determine prices of European and American exchange options when underlying asset prices are modelled with stochastic volatility and jump-diffusion dynamics. As the MOL, as with any other…