Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier is hit that would render the claim worthless afterwards, is challenging. All hedging methods potentially lead to large errors when the underlying is already close to the barrier and the...

This study compares the performances of neural network and Black-Scholes models in pricing BIST30 (Borsa Istanbul) index call and put options with different volatility forecasting approaches. Since the volatility is the key parameter in pricing options, GARCH (Generalized Autoregressive...

Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier is hit that would render the claim worthless afterwards, is challenging. All hedging methods potentially lead to large errors when the underlying is already close to the barrier and the...

In this paper, we show that a time-dependent local stochastic volatility (SLV) model can be reduced to a system of autonomous PDEs that can be solved using the heat kernel, by means of the Wei-Norman factorization method and Lie algebraic techniques. Then, we compare the results of traditional...

The hedging argument of Black and Scholes (1973) hinges on the assumption that a continuously rebalanced asset portfolio satisfies the continuous-time self-financing condition. This condition, which is a special case of the continuous-time budget equation of Merton (1971), is believed to...

We study the capability of arbitrage-free neural-SDE market models to yield effective strategies for hedging options. In particular, we derive sensitivity-based and minimum-variance-based hedging strategies using these models and examine their performance when applied to various option...

We propose a new jump-diffusion process, the Heston-Queue-Hawkes (HQH) model, combining the well-known Heston model and the recently introduced Queue-Hawkes (Q-Hawkes) jump process. Like the Hawkes process, the HQH model can capture the effects of self-excitation and contagion. However, since...

This paper derives explicit expressions to simulate theta and gamma for American options using the pathwise derivative method. While the pathwise derivative formulas for delta, rho, and vega of American options have been studied in the literature, no correct explicit results for theta and gamma...

We examine the distribution of realized Bitcoin daily log-returns and find significantly-thin tails. From there we construct a simple connection back to traditional volatility modelling. And then we discuss how this connection can serve as a foundation to leverage existing derivative quant...

Changes in stock prices, both when the stock price increases or decreases in price, can be used to gain profits. One of the investment instruments that can be used to profit from changes in stock prices is stock options. In addition, stock options can also be used to minimize the amount of loss...

Volatility Skew and Smile of Interest Rate products (Swaption and Caplet) are represented by SABR (Stochastic Alpha Beta Rho model). So, the Interest Rate derivatives model for pricing the callable exotic swaps should be comparable to the SABR volatility surface. In the interest rate derivatives...

The literature on dynamic option valuation typically does not explicitly specify a pricing kernel. Instead it characterizes the kernel indirectly by specifying prices of risk, or defines it implicitly as the ratio of the risk-neutral and physical probabilities. We propose explicit pricing...

We show that a structural model of firm decisions can produce very flexible implied volatility surfaces: upward and downward sloping, u-shaped. A calibrated version of the model is able to match many unconditional financial characteristics of the average option-able stock, and can help explain...

This research proposes a new option pricing model. The model revises the unimodal probability distribution assumption used in the past, and proposes a bimodal probability distribution for option pricing. The bimodal probability distribution proposed in this study can be degenerated to a unimodal...

We analyse robust dynamic delta hedging of bitcoin options using a set of smile-implied and other smile-adjusted deltas that are either model-free, in the sense that they are the same for every scale-invariant stochastic and/or local volatility model, or they are based on simple regime-dependent...

The article describes a global and arbitrage-free parametrization of the eSSVI surfaces introduced by Hendriks and Martini in 2019. A robust calibration of such surfaces has already been proposed by the quantitative research team at Zeliade in 2019, but it is sequential in expiries and lacks of...

If a discretely formulated asset pricing model rivals efficacy of the Black and Scholes (1973) option pricing model, with canonical properties of option prices satisfied, rather counterfactually it spans a support space for call option prices that is continuous. Absent any directness of modeling...

In 1973, Fischer Black and Myron Scholes published their seminal work on options pricing. Their model relied on a clever hedge which seemingly resulted in a risk-free portfolio. However, further analysis of this portfolio reveals that it may not be risk-free at all. A truly risk-free portfolio...

We devise a method to circumvent the complexity that arises from the option multi-dimensionality. That is, we transform the model to make it as simple as the one-dimensional case. Furthermore, the assumption of comonotonicity and other assumptions regarding the structure of the underlying asset...

Since their introduction, quanto options have steadily gained popularity. Matching Black-Scholes-type pricing models and, more recently, a fat-tailed, normal tempered stable variant have been established. The objective here is to empirically assess the adequacy of quanto-option pricing models....

We examine the connection between discrete-time models of financial markets and the celebrated Black--Scholes--Merton (BSM) continuous-time model in which ''markets are complete." Suppose that (a) the probability law of a sequence of discrete-time models converges to the law of the BSM model and...

The recently developed Bitcoin futures and options contracts in cryptocurrency derivatives exchanges mark the beginning of a new era in Bitcoin price risk hedging. The need for these tools dates back to the market crash of 1987, when investors needed better ways to protect their portfolios...

This paper investigates the American option price in a two-state regime-switching model. The dynamics of underlying are driven by a Markov-modulated Geometric Wiener process. That means the interest rate, the appreciation rate, and the volatility of underlying rely on hidden states of the...

A family of Exponentially Fitted Block Backward Differentiation Formulas (EFBBDFs) whose coefficients depend on a parameter and step-size is developed and implemented on the Black-Scholes partial differential equation (PDE) for the valuation of options on a non-dividend-paying stock. Specific...

We introduce a novel approach to capture implied volatility smiles. Given any parametric option pricing model used to fit a smile, we train a deep feedforward neural network on the model's orthogonal residuals to correct for potential mispricings and boost performance. Using a large number of...

We consider a slight extension of the constant volatility Black-Scholes model where the integrated variance is assumed random, uncorrelated to the spot process and uniformly distributed over a finite range. We analytically calculate the expectation over the random variance and obtain a closed...

To cope with the negative oil futures price caused by the COVID-19 recession, global commodity futures exchanges switched the option model from Black-Scholes to Bachelier in April 2020. This study reviews the literature on Bachelier's pioneering option pricing model and summarizes the practical...

We provide explicit, simple price formulas for the Europeanoptions under stochastic volatility and stochastic interest rate. The formulasare as simple as the classical Black-Scholes formula. Moreover, the formulasdo not require the normality of the returns. We do not need to know thedistribution...

We devise a method to circumvent the complexity that arises from the option multi-dimensionality. That is, we transform the model to make it as simple as the one-dimensional case. Furthermore, the assumption of comonotonicity and other assumptions regarding the structure of the underlying asset...

For a sample of financial intermediaries from the US, we show that corporate value is strongly related to (risk-neutral) option-implied skewness. In contrast, historical (return-based) skewness does not play a role for valuation. We illustrate that the option-implied skewess predicts better...

Modelling correlation between financial quantities is important in the accurate pricing of financial derivatives. In this paper, we introduce some stochasticity in correlation, by considering a regime-switching correlation model, in which the transition rates between regimes are given. We...

We show that a dynamic model of investment and capital structure choices, where the firm faces real and financial frictions, can generate option prices and implied volatilities that are in line with those of the average optionable stock. As the balance between the fundamental economic forces...

We devise a method to circumvent the complexity that arises from the option multi-dimensionality. That is, we transform the model to make it as simple as the one-dimensional case. Furthermore, the assumption of comonotonicity and other assumptions regarding the structure of the underlying asset...

When investing in derivatives portfolios (such as options), the delta-gamma approximation (DGA) is often used as a risk management strategy to reduce the risk associated with the underlying asset price. However, this approximation is accepted only for small changes of the underlying asset price....

This article investigates the delta hedging performance of the skewness and kurtosis adjusted Black-Scholes model of Corrado and Su (1996) and Brown and Robinson (2002). The empirical tests in the FTSE 100 index option market show that the more sophisticated skewness and kurtosis adjusted model...