An exact closed-form pricing formula was derived for American options when stock returns follow a normal distribution or Lévy processes. It uses a new non-homogeneous partial differential equation for American options, the condition from optimal early exercise general solution, and hence a...

Prices of financial options in a market with liquidity risk are shown to be weak solutions of a class of semilinear parabolic partial differential equations with nonnegative characteristic form. We prove the existence and uniqueness of such solutions, and then show the solutions correspond to...

We apply the Malliavin calculus to the stochastic string framework and obtain a Clark-Ocone-like formula. This result allows us to rewrite the hedging portfolio explicitly in terms of the Malliavin derivative of the discounted payoff. We illustrate this new result with two applications. Firstly,...

Simple analytical solutions for the prices of discretely monitored barrier options do not yet exist in the literature. This paper presents a semi-analytical and fully explicit solution for pricing discretely monitored barrier options when the underlying asset is driven by a general Lévy...

Closed-form pricing formulae and option Greeks are obtained for European-type options using an orthogonal polynomial series -- complex Fourier series. We assume that risky assets are driven by exponential Lévy processes and stochastic volatility models. We provide a succinct error analysis to...

Can-Do Options are derivative products listed on the JSE's derivative exchanges -- mostly equity derivative products listed on Safex and currency derivative products listed on Yield-X. These products give investors the advantages of listed derivatives with the flexibility of over the counter...

Option pricing literature is usually concerned with financial contracts whose payoffs depend on decisions by only one of the contract's parties. Generalizations to more complex cases with decisions by both parties are impeded by the ad-hoc nature of many contributions. One prominent example...

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 develop approximate formulae expressed in terms of elementary functions for the density, the price and the Greeks of path dependent options of Asian style, in a general local volatility model. An algorithm for computing higher order approximations is provided. The proof is based on a heat...

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...