Related papers: Counterexamples for FX Options Interpolations -- P…
The Chicago Board Options Exchange (CBOE) Volatility Index, VIX, is calculated based on prices of out-of-the-money put and call options on the S&P 500 index (SPX). Sometimes called the "investor fear gauge," the VIX is a measure of the…
In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically…
Interpolated multiple zeta values can be regarded as interpolation polynomials of multiple zeta values and multiple zeta-star values. In this paper, we give some algebraic relations of interpolated multiple zeta values, such as the…
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call…
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…
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations…
The pricing of currency options is largely dependent on the dynamic relationship between a pair of currencies. Typically, the pricing of options with payoffs dependent on multi-assets becomes tricky for reasons such as the non-Gaussian…
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 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…
This paper investigates problems associated with the valuation of callable American volatility put options. Our approach involves modeling volatility dynamics as a mean-reverting 3/2 volatility process. We first propose a pricing formula…
It is well known that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and…
In this article, we consider the small-time asymptotics of options on a \emph{Leveraged Exchange-Traded Fund} (LETF) when the underlying Exchange Traded Fund (ETF) exhibits both local volatility and jumps of either finite or infinite…
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…
We show that capital flow (CF) volatility exerts an adverse effect on exchange rate (FX) volatility, regardless of whether capital controls have been put in place. However, this effect can be significantly moderated by certain macroeconomic…
A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. Typically, this (inverse) problem is solved in a two step procedure : (i) a smooth parametrization of the implied…
We present a general derivation of the arbitrage-free pricing framework for multiple-currency collateralized products. We include the impact on option pricing of the policy adopted to fund in foreign currency, so that we are able to price…
We show that time-dependent fluctuations $\{\Delta x\}$ in foreign exchange rates are accurately described by a random walk in a complex plane that is demarcated into the gain (+) and loss (-) sectors. $\{\Delta x\}$ is the outcome of $N$…
We discuss price variations distributions in foreign exchange markets, characterizing them both in calendar and business time frameworks. The price dynamics is found to be the result of two distinct processes, a multi-variance diffusion and…
In this paper, the extended double shuffle relations for interpolated multiple zeta values are established. As an application, Hoffman's relations for interpolated multiple zeta values are proved. Furthermore, a generating function for sums…
This paper derives explicit formulas for both the small and large time limits of the implied volatility in the minimal market model. It is shown that interest rates do impact on the implied volatility in the long run even though they are…