Related papers: Tail Option Pricing Under Power Laws
For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by…
This paper investigates how two important sources of risk -- market tail risk and extreme market volatility risk -- are priced into the cross-section of asset returns across various investment horizons. To identify such risks, we propose a…
The influence of Commodity Trading Advisors (CTA) on the price process is explored with the help of a simple model. CTA managers are taken to be Kelly optimisers, which invest a fixed proportion of their assets in the risky asset and the…
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…
In this paper we extend the theory of option pricing to take into account and explain the empirical evidence for asset prices such as non-Gaussian returns, long-range dependence, volatility clustering, non-Gaussian copula dependence, as…
The notion of tail adversarial stability has been proven useful in obtaining limit theorems for tail dependent time series. Its implication and advantage over the classical strong mixing framework has been examined for max-linear processes,…
Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…
We introduce signature payoffs, a family of path-dependent derivatives that are given in terms of the signature of the price path of the underlying asset. We show that these derivatives are dense in the space of continuous payoffs, a result…
We consider a financial market in which two securities are traded: a stock and an index. Their prices are assumed to satisfy the Black-Scholes model. Besides assuming that the index is a tradable security, we also assume that it is…
We derive the implied volatility estimation formula in European power call options pricing, where the payoff functions are in the form of $V=(S^{\alpha}_T-K)^{+}$ and $V=(S^{\alpha}_T-K^{\alpha})^{+}$ ($\alpha>0$)respectively. Using…
The general and special repo rates are related with the prices of the European call- and American put-options. The evaluation takes into account specific business models of the parties in the repo agreement and the law restrictions. Using…
We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation…
The paper focuses on pricing European-style options on several underlying assets under the Black-Scholes model represented by a nonstationary partial differential equation. The proposed method combines the Galerkin method with…
In the presence of a layer of metaprobabilities (from uncertainty concerning the parameters), the asymptotic tail exponent corresponds to the lowest possible tail exponent regardless of its probability. The problem explains "Black Swan"…
We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the…
Power law distributions, in particular Pareto distributions, describe data across diverse areas of study. We have developed a package in R to estimate the tail index for such datasets focusing on speed (in particular with large datasets),…
We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments…
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…
This article considers the pricing and hedging of a call option when liquidity matters, that is, either for a large nominal or for an illiquid underlying asset. In practice, as opposed to the classical assumptions of a price-taking agent in…
We consider plain vanilla European options written on an underlying asset that follows a continuous time semi-Markov multiplicative process. We derive a formula and a renewal type equation for the martingale option price. In the case in…