We propose a new accurate method for pricing European spread options by extending the lower bound approximation of Bjerksund and Stensland (2011) beyond the classical Black-Scholes framework. This is possible via a procedure requiring a univariate Fourier inversion. In addition, we are also able...

Options on futures traded in Europe, Australia and South Africa are subject to futures-style premium posting (FSPP): the premium is not paid up front but marked to market, and the last settlement premium paid upon exercise. The previous literature has derived pricing models for such options....

This paper introduces an option pricing algorithm based on non-orthogonal series expansion methods. More precisely, Gabor frame decomposition is used to split the risk neutral option pricing formula into the sum of two inner products that can be evaluated efficiently by means of Parseval's...

In some papers we remarked that derivation of the Black Scholes Equation (BSE) contains mathematical ambiguities. In particular, there are two problems which can be raised by accepting Black Scholes (BS) pricing concept. One is technical derivation of the BSE and the other the pricing definition...

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...

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...

An option market maker incurs funding costs when carrying and hedging inventory. To hedge a net long delta inventory, for example, she pays a fee to borrow stock from the security lending market. Because of haircuts, she posts additional cash margin to the lender which needs to be financed at...

Investment behaviour, techniques and choices have evolved in the options markets since the launch of options trading in 1973. Today, we are entering the field of Big Data and the explosion of information, which has become the main feature of science, impacts investors' decisions and their...

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...

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...