Derivatives pricing with marked point processes using Tick-by-tick dataR

I propose to model stock price tick-by-tick data via a non-explosive marked point process. The arrival of trades is driven by a counting process in which the waiting-time between trades possesses a Mittag-Leffler survival function and price revisions have an infinitely divisible distribution. I show that the partial-integro-differential equation satisfied by the value of European-style derivatives contains a non-local operator in time-to-maturity known as the Caputo fractional derivative. Numerical examples are provided for a marked point process with conditionally Gaussian and with conditionally CGMY price innovations. Furthermore, the infinitesimal generator of the marked point process derived to price derivatives coincides with that of a Lévy process of either finite or infinite activity.Tick-by-tick data, Waiting-times, Duration, High frequency data, Caputo operator, Marked point process,

A Hedged Monte Carlo Approach to Real Option Pricing

In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or subjective) measure in a possibly incomplete market. Our approach is suitable also to incorporating subjective views from management or market experts and to stochastic investment costs. It is based on the Hedged Monte Carlo strategy proposed by Potters et al (2001) where options are priced simultaneously with the determination of the corresponding hedging. The approach is particularly well-suited to the evaluation of commodity related projects whereby the availability of pricing formulae is very rare, the scenario simulations are usually available only in the historical measure, and the cash flows can be highly nonlinear functions of the prices.Comment: 25 pages, 14 figure

Change of numéraire for affine arbitrage pricing models driven by multifactor marked point processes.

We derive a general formula for the change of numéraire in multifactor ane arbitrage free models driven by marked point processes. As a complement, we present both ane structures and change of measures in the general setting of jump diusions. This provides for a comprehensive view on the subject.

Monte Carlo derivative pricing with partial information in a class of doubly stochastic Poisson processes with marks

To model intraday stock price movements we propose a class of marked doubly stochastic Poisson processes, whose intensity process can be interpreted in terms of the effect of information release on market activity. Assuming a partial information setting in which market agents are restricted to observe only the price process, a filtering algorithm is applied to compute, by Monte Carlo approximation, contingent claim prices, when the dynamics of the price process is given under a martingale measure. In particular, conditions for the existence of the minimal martingale measure Q are derived, and properties of the model under Q are studied.Minimal martingale measure, News arrival, Marked point process, Nonlinear filtering, Reversible jump Markov chain Monte Carlo, Ultra high frequency data

Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts

In this paper, we study the benefits of using polyharmonic splines and node layouts with smoothly varying density for developing robust and efficient radial basis function generated finite difference (RBF-FD) methods for pricing of financial derivatives. We present a significantly improved RBF-FD scheme and successfully apply it to two types of multidimensional partial differential equations in finance: a two-asset European call basket option under the Black--Scholes--Merton model, and a European call option under the Heston model. We also show that the performance of the improved method is equally high when it comes to pricing American options. By studying convergence, computational performance, and conditioning of the discrete systems, we show the superiority of the introduced approaches over previously used versions of the RBF-FD method in financial applications

Error analysis of truncated expansion solutions to high-dimensional parabolic PDEs

We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of dominant principal components. The focus of the present article is the derivation of sharp error bounds for the constant coefficient case and a first and second order approximation. We give a precise characterisation when these bounds hold for (non-smooth) option pricing applications and provide numerical results demonstrating that the practically observed convergence speed is in agreement with the theoretical predictions

Nonparametric estimates of pricing functionals

We analyze the empirical performance of several non-parametric estimators of the pricing functional for European options, using historical put and call prices on the S&P500 during the year 2012. Two main families of estimators are considered, obtained by estimating the pricing functional directly, and by estimating the (Black-Scholes) implied volatility surface, respectively. In each case simple estimators based on linear interpolation are constructed, as well as more sophisticated ones based on smoothing kernels, \`a la Nadaraya-Watson. The results based on the analysis of the empirical pricing errors in an extensive out-of-sample study indicate that a simple approach based on the Black-Scholes formula coupled with linear interpolation of the volatility surface outperforms, both in accuracy and computational speed, all other methods

Empirical Tests of Models of Catastrophe Insurance Futures

The authors empirically investigate models of insurance futures derivatives contracts. In the fall of 1993 the Chicago Board of Trade (CBOT) started trading a contract designed to scrutinize catastrophic risk, which is currently done in the reinsurance markets. There are obvious advantages to trading on organized exchanges (standardization, liquidity, much reduced credit risk, etc.) as opposed to OTC markets. There has so far been little academic on these contracts. In this paper we look at the price history for the first two years within the context of a pricing model of Aase [1995]. This paper was presented at the Financial Institutions Center's May 1996 conference on "

A note on intraday option pricing

Compound renewal processes can be used as an approximate phenomenological model of tick-by-tick price fluctuations. An exact and explicit general formula is derived for the martingale price of a European call option written on a compound renewal process. The option price is obtained using the direct method of indicator functions. The applicability of this result is discussed