Related papers: Option market (in)efficiency and implied volatilit…
We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk…
In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries…
It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset…
The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…
We introduce a stochastic price model where, together with a random component, a moving average of logarithmic prices contributes to the price formation. Our model is tested against financial datasets, showing an extremely good agreement…
Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged…
We revisit the foundational Moment Formula proved by Roger Lee fifteen years ago. We show that when the underlying stock price martingale admits finite log-moments E[|log(S)|^q] for some positive q, the arbitrage-free growth in the left…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
We apply a utility-based method to obtain the value of a finite-time investment opportunity when the underlying real asset is not perfectly correlated to a traded financial asset. Using a discrete-time algorithm to calculate the…
Stochastic volatility models describe asset prices $S_t$ as driven by an unobserved process capturing the random dynamics of volatility $\sigma_t$. Here, we quantify how much information about $\sigma_t$ can be inferred from asset prices…
Corporate earnings announcements unpack large bundles of public information that should, in efficient markets, trigger jumps in stock prices. Testing this implication is difficult in practice, as it requires noisy high-frequency data from…
The growth of the exhange-traded fund (ETF) industry has given rise to the trading of options written on ETFs and their leveraged counterparts {(LETFs)}. We study the relationship between the ETF and LETF implied volatility surfaces when…
We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…
We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a…
In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used…
We correct a mistake in the published version of our paper. Our new conclusion is that the "implied leverage effect" for single stocks is underestimated by option markets for short maturities and overestimated for long maturities, while it…
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a…
Stylized facts can be regarded as constraints for any modeling attempt of price dynamics on a financial market, in that an empirically reasonable model has to reproduce these stylized facts at least qualitatively. The dynamics of market…
We study a new measure of codependency in the second moment of a continuous-time multivariate asset price process, which we name the realized copula of volatility. The statistic is based on local volatility estimates constructed from…
We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…