Related papers: Counterexamples for FX Options Interpolations -- P…
This article explores the relationship between the SPX and VIX options markets. High-strike VIX call options are used to hedge tail risk in the SPX, which means that SPX options are a reflection of the extreme-strike asymptotics of VIX…
This paper aims at solving FX market volatility modeling problem and finding the most becoming approach to this task. Validity of two competing approaches, classical econometric generalized conditional heteroscedasticity and mathematical…
There are no known exact formulas for the valuation of a number of exotic options, and this is particularly true for options under discrete monitoring and for American style options. Therefore, one usually recourses to a Monte Carlo…
Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range…
The quanto option is a cross-currency derivative in which the pay-off is given in foreign currency and then converted to domestic currency, through a constant exchange rate, used for the conversion and determined at contract inception.…
In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it…
The implied volatility is a crucial element of any financial toolbox, since it is used for quoting and the hedging of options as well as for model calibration. In contrast to the Black-Scholes formula its inverse, the implied volatility, is…
Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the…
We consider a novel use case for the Double Heston model (Christoffersen et al,, 2009), where the two Heston sub-variances have different spot/volatility correlations but the same volatility of volatility and mean reversion speed. This…
It is well-known that, in the Bachelier model, when asset prices and volatilities are uncorrelated, the implied volatility coincides with the fair value of the volatility swap. In this paper, via classical It\^o calculus and Taylor…
We develop closed-form expansions for the implied volatility of VIX options within the class of forward variance models. Our approach builds on weak-approximation techniques for VIX option prices and yields explicit implied volatility…
In previous works Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all…
This article presents a generic hybrid numerical method to price a wide range of options on one or several assets, as well as assets with stochastic drift or volatility. In particular for equity and interest rate hybrid with local…
After a market downturn, especially in an uncertain economic environment such as the current state, there can be a relatively long period with a sideways market, where indexes, stocks, etc., move in channels with support and resistance…
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 consider a general local-stochastic volatility model and an investor with exponential utility. For a European-style contingent claim, whose payoff may depend on either a traded or non-traded asset, we derive an explicit approximation for…
It is commonly accepted that Commodities futures and forward prices, in principle, agree under some simplifying assumptions. One of the most relevant assumptions is the absence of counterparty risk. Indeed, due to margining, futures have…
We introduce a simple stochastic volatility model, whose novelty consists in taking into account hitting times of the asset price, and study the optimal stopping problem corresponding to a put option whose time horizon (after the asset…
The role of collateral in derivative pricing has evolved beyond credit risk mitigation, particularly following the global financial crisis, when funding costs and basis spreads became central to valuation practices. This development…
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…