Compound options are options for which the underlying is another option. In other words, a compound option is an option written on an option. In this paper, we present two new approaches to compound option pricing. The first approach relies on Malliavin calculus methods and the Clark-Ocone...

The market for ultra short-term (zero days-to-expiry or 0DTE) options has grown exponentially over the last few years. In 2023, daily volume in 0DTEs reached over 45% of overall daily options volume. After briefly describing this exploding new market, we present a novel pricing formula designed...

In this paper, I have used simple arbitrage argument to derive a dozen of model-free option price properties. In addition to deriving the Greeks under the model-free framework, the results show that first, in contrast to the traditional view, a European call (put) option for a...

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...

It has been demonstrated that European option premia computed with a binomial lattice, as first described by Cox, Ross, and Rubinstein (CRR, 1979), do not have a closed-form solution (Georgiadis, 2011). This stems from a lack of hypergeometricity, an artifact of Gosper's algorithm, and naturally...

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VωAPut(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is...

This paper discusses how to obtain the Black-Scholes equation to evaluate options and how to obtain explicit solutions for Call and Put. The Black-Scholes equation, which is the basis for determining explicit solutions for Call and Put, is a rather sophisticated equation. It is a partial...

In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman in 1997 to price a π-option. This method is based on the simulated price tree that comes from discretization and replication of possible trajectories of the underlying asset's price. As a result, this algorithm...

I document a sizeable bias that might arise when valuing out of the money American options via the Least Square Method proposed by Longstaff and Schwartz (2001). The key point of this algorithm is the regression-based estimate of the continuation value of an American option. If this regression...

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...