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Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

Milev, Mariyan, Tagliani, Aldo (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 65M06, 65M12.In this paper we explore the numerical diffusion introduced by two nonstandard finite difference schemes applied to the Black-Scholes partial differential equation for pricing discontinuous payoff and low volatility options. Discontinuities in the initial conditions require applying nonstandard non-oscillating finite difference schemes such as the exponentially fitted finite difference schemes suggested by D. Duffy and the Crank-Nicolson variant...

Newsboy Problem: Viability of Optimal Initial Selling Price and Ordering Policies in the Presence of Exogenous Price Decline and Random Lead Time

Ningombam Sanjib Meitei, Snigdha Banerjee (2013)

RAIRO - Operations Research - Recherche Opérationnelle

Analysis of empirical sales data lead us to consider newsboy model for four practical market conditions arising from the presence/absence of stochastic lead time and exogenous linear temporal decline in selling price when distribution of the stochastic demand depends upon initial selling price. Viability of the solutions is discussed for three strategies of obtaining optimal initial selling price and/or ordering quantity. Numerical studies are conducted to assess the effects of lead time and price...

Nonexpansive maps and option pricing theory

Vassili N. Kolokoltsov (1998)

Kybernetika

The famous Black–Sholes (BS) and Cox–Ross–Rubinstein (CRR) formulas are basic results in the modern theory of option pricing in financial mathematics. They are usually deduced by means of stochastic analysis; various generalisations of these formulas were proposed using more sophisticated stochastic models for common stocks pricing evolution. In this paper we develop systematically a deterministic approach to the option pricing that leads to a different type of generalisations of BS and CRR formulas...

Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

Milev, Mariyan, Tagliani, Aldo (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 65M06, 65M12.The paper is devoted to pricing options characterized by discontinuities in the initial conditions of the respective Black-Scholes partial differential equation. Finite difference schemes are examined to highlight how discontinuities can generate numerical drawbacks such as spurious oscillations. We analyze the drawbacks of the Crank-Nicolson scheme that is most frequently used numerical method in Finance because of its second order accuracy....

Numerical solution of Black-Scholes option pricing with variable yield discrete dividend payment

Rafael Company, Lucas Jódar, Enrique Ponsoda (2008)

Banach Center Publications

This paper deals with the construction of numerical solution of the Black-Scholes (B-S) type equation modeling option pricing with variable yield discrete dividend payment at time t d . Firstly the shifted delta generalized function δ ( t - t d ) appearing in the B-S equation is approximated by an appropriate sequence of nice ordinary functions. Then a semidiscretization technique applied on the underlying asset is used to construct a numerical solution. The limit of this numerical solution is independent of the...

Oligopoly Model of a Debit Card Network

Manchev, Peter (2007)

Serdica Mathematical Journal

JEL Classification: G21, L13.The paper builds an oligopoly model of a debit card network. It examines the competition between debit card issuers. We show that there is an optimal pricing for the debit card network, which maximizes all issuer’s revenues. The paper also shows that establishing a link between debit card networks averages the costs provided that there is no growth in the customer’s usage of the networks, resulting from the link.

On European option pricing under partial information

Meng Wu, Jue Lu, Nan-jing Huang (2016)

Applications of Mathematics

We consider a European option pricing problem under a partial information market, i.e., only the security's price can be observed, the rate of return and the noise source in the market cannot be observed. To make the problem tractable, we focus on gap option which is a generalized form of the classical European option. By using the stochastic analysis and filtering technique, we derive a Black-Scholes formula for gap option pricing with dividends under partial information. Finally, we apply filtering...

On option pricing in the multidimensional Cox-Ross-Rubinstein model

Michał Motoczyński, Łukasz Stettner (1998)

Applicationes Mathematicae

Option pricing in the multidimensional case, i.e. when the contingent claim paid at maturity depends on a number of risky assets, is considered. It is assumed that the prices of the risky assets are in discrete time subject to binomial disturbances. Two approaches to option pricing are studied: geometric and analytic. A numerical example is also given.

On valuation of derivative securities: A Lie group analytical approach

Phillip S. C. Yam, Hailiang Yang (2006)

Applications of Mathematics

This paper proposes a Lie group analytical approach to tackle the problem of pricing derivative securities. By exploiting the infinitesimal symmetries of the Boundary Value Problem (BVP) satisfied by the price of a derivative security, our method provides an effective algorithm for obtaining its explicit solution.

Optimality of the replicating strategy for American options

Marek Kociński (1999)

Applicationes Mathematicae

The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox-Ross-Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an optimal replicating strategy that is not optimal in the global sense.

Currently displaying 41 – 60 of 76