相关论文: On the Consistency of the Deterministic Local Vola…
Recent studies have demonstrated the efficiency of Variational Autoencoders (VAE) to compress high-dimensional implied volatility surfaces into a low dimensional representation. Although this method can be effectively used for pricing…
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…
We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include…
Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on…
We prove that a wide class of correlated stochastic volatility models exactly measure an empirical fact in which past returns are anticorrelated with future volatilities: the so-called ``leverage effect''. This quantitative measure allows…
A common approach to valuing exotic options involves choosing a model and then determining its parameters to fit the volatility surface as closely as possible. We refer to this as the model calibration approach (MCA). A disadvantage of MCA…
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic…
We propose an artificial market model based on deterministic agents. The agents modify their ask/bid price depending on past price changes. The temporal development of market price fluctuations is calculated numerically. A probability…
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional…
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…
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…
Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of…
Prepayment risk embedded in fixed-rate mortgages forms a significant fraction of a financial institution's exposure. The embedded prepayment option bears the same interest rate risk as an exotic interest rate swap with a suitable stochastic…
It has been assumed that arbitrage profits are not possible in efficient markets, because future prices are not predictable. Here we show that predictability alone is not a sufficient measure of market efficiency. We instead propose to…
We consider the following problem in stochastic portfolio theory. Are there portfolios that are relative arbitrages with respect to the market portfolio over very short periods of time under realistic assumptions? We answer a slightly…
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…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk…
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However,…
This paper studies convex duality in optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions…