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A detailed analysis of correlation between stock returns at high frequency is compared with simple models of random walks. We focus in particular on the dependence of correlations on time scales - the so-called Epps effect. This provides a…
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
We consider a finite horizon optimal stopping problem related to trade-off strategies between expected profit and cost cash-flows of an investment under uncertainty. The optimal problem is first formulated in terms of a system of Snell…
Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
Observing prices of European put and call options, we calibrate exponential L\'evy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for L\'evy models of finite jump activity as well as…
This paper examines the problem of pricing spread options under some models with jumps driven by Compound Poisson Processes and stochastic volatilities in the form of Cox-Ingersoll-Ross(CIR) processes. We derive the characteristic function…
Based on the existing literature, this article presents the different ways of choosing the parameters of stochastic volatility models in general, in the context of pricing financial derivative contracts. This includes the use of stochastic…
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…
In this paper we study short-time behavior of the at-the-money implied volatility for Inverse European options with fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques of the…
We present a theory of option pricing and hedging, designed to address non-perfect arbitrage, market friction and the presence of `fat' tails. An implied volatility `smile' is predicted. We give precise estimates of the residual risk…
Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to…
We study the relation between stock price changes and the difference in the number of sell and buy orders. Using a soft spin model, we describe the price impact of order imbalances and find an analogy to the fluctuation-dissipation theorem…
In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semi-static portfolios should more properly be thought of as separate classes of derivatives, with non-trivial,…
We prove a scaling limit theorem for the super-replication cost of options in a Cox--Ross--Rubinstein binomial model with transient price impact. The correct scaling turns out to keep the market depth parameter constant while resilience…
We study the Option pricing with linear investment strategy based on discrete time trading of the underlying security, which unlike the existing continuous trading models provides a feasible real market implementation. Closed form formulas…
Recent empirical evidence has highlighted the crucial role of jumps in both price and volatility within the cryptocurrency market. In this paper, we integrate price--volatility co-jumps and volatility short-term dependency into a coherent…
It is well known that any sufficiently regular one-dimensional payoff function has an explicit static hedge by bonds, forward contracts and lots of vanilla options. We show that the natural extension of the corresponding representation…
The coupled system, where one is a degenerate parabolic equation and the other has not a diffusion term arises in the modeling of European options with liquidity shocks. Two implicit-explicit (IMEX) schemes that preserve the positivity of…
This book chapter illustrates how to apply extreme value statistics to financial time series data. Such data often exhibits strong serial dependence, which complicates assessment of tail risks. We discuss the two main approches to tail risk…