Related papers: Normalization for Implied Volatility
Volatility smile and skewness are two key properties of option prices that are represented by the implied volatility (IV) surface. However, IV surface calibration through nonlinear interpolation is a complex problem due to several factors,…
This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock's price. Thus, we consider a…
This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of Markov-modulated regime…
We investigate whether it is possible to formulate option pricing and hedging models without using probability. We present a model that is consistent with two notions of volatility: a historical volatility consistent with statistical…
We consider a non-stochastic online learning approach to price financial options by modeling the market dynamic as a repeated game between the nature (adversary) and the investor. We demonstrate that such framework yields analogous…
We consider the Black--Scholes model of financial market modified to capture the stochastic nature of volatility observed at real financial markets. For volatility driven by the Ornstein--Uhlenbeck process, we establish the existence of…
The coupled system, where one is a degenerate parabolic equation and the other has not a diffusion term arises in the modeling of European options with liquidity shocks. Two implicit-explicit (IMEX) schemes that preserve the positivity of…
We develop a novel observation-driven model for high-frequency prices. We account for irregularly spaced observations, simultaneous transactions, discreteness of prices, and market microstructure noise. The relation between trade durations…
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to…
Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. This paper is an attempt to extend their work to a situation in which the…
We propose a deep hedging framework for index option portfolios, grounded in a realistic market simulator that captures the joint dynamics of S&P 500 returns and the full implied volatility surface. Our approach integrates surface-informed…
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…
We investigate the asymptotic behaviour of the implied volatility in the Bachelier setting, extending the large-strike results established for the Black-Scholes framework. Exploiting the theory of regular variation, we derive explicit…
This paper derives integral representations for the Black-Scholes price of arithmetic-average Asian options. Their proof is by Laplace inverting the 1992 Laplace transform of Geman-Yor using complex analytic methods. The analysis ultimately…
Closed form formulas for swaption prices in HJM model are derived. These formulas are used for nonparametric fit of deterministic forward volatility. It is demonstrated that this formula and non-parametric fit works very well and can be…
We train neural networks to learn optimal replication strategies for an option when two replicating instruments are available, namely the underlying and a hedging option. If the price of the hedging option matches that of the Black--Scholes…
We provide an European option pricing formula written in the form of an infinite series of Black Scholes type terms under double Levy jumps model, where both the interest rate and underlying price are driven by Levy process. The series…
In this paper we introduce the concept of standardized call function and we obtain a new approximating formula for the Black and Scholes call function through the hyperbolic tangent. This formula is useful for pricing and risk management as…
The dynamics of market prices is described as the evolution of opinions in the trading community regarding future market behavior. The price then is a function of the voting process of the market players in favor to raise or reduce the…
We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and…