A variational inequality from pricing convertible bond.
Actuarial Approach to Option Pricing in a Fractional Black-Scholes Model with Time-Dependent Volatility
We study actuarial methods of option pricing in a fractional Black-Scholes model with time-dependent volatility. We interpret the option as a potential loss and we show that the fair premium needed to insure this loss coincides with the expectation of the discounted claim payoff under the average risk neutral measure.
Adaptive predictions of the euro/złoty currency exchange rate using state space wavelet networks and forecast combinations
The paper considers the forecasting of the euro/Polish złoty (EUR/PLN) spot exchange rate by applying state space wavelet network and econometric forecast combination models. Both prediction methods are applied to produce one-trading-dayahead forecasts of the EUR/PLN exchange rate. The paper presents the general state space wavelet network and forecast combination models as well as their underlying principles. The state space wavelet network model is, in contrast to econometric forecast combinations,...
Almost log-optimal trading strategies for small transaction costs in model with stochastic coefficients
We consider a non-consuming agent investing in a stock and a money market interested in the portfolio market price far in the future. We derive a strategy which is almost log-optimal in the long run in the presence of small proportional transaction costs for the case when the rate of return and the volatility of the stock market price are bounded It o processes with bounded coefficients and when the volatility is bounded away from zero.
An American convert close to maturity.
An analytic solution for a Vasicek interest rate convertible bond model.
An application of dynamic programming principle in corporate international optimal investment and consumption choice problem.
An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model
We consider the pricing of credit default swaps (CDSs) with the reference asset assumed to follow a geometric Brownian motion with a fast mean-reverting stochastic volatility, which is often observed in the financial market. To establish the pricing mechanics of the CDS, we set up a default model, under which the fair price of the CDS containing the unknown “no default” probability is derived first. It is shown that the “no default” probability is equivalent to the price of a down-and-out binary...
An asset – liability management stochastic program of a leasing company
We build a multi-stage stochastic program of an asset-liability management problem of a leasing company, analyse model results and present a stress-testing methodology suited for financial applications. At the beginning, the business model of such a company is formulated. We introduce three various risk constraints, namely the chance constraint, the Value-at-Risk constraint and the conditional Value-at-Risk constraint along with the second-order stochastic dominance constraint, which are applied...
An Expert System for Ranking Companies and Investments: Wood Industry Case
An explicit solution for optimal investment problems with autoregressive prices and exponential utility
We calculate explicitly the optimal strategy for an investor with exponential utility function when the price of a single risky asset (stock) follows a discrete-time autoregressive Gaussian process. We also calculate its performance and analyse it when the trading horizon tends to infinity. Dependence of the asymptotic performance on the autoregression parameter is determined. This provides, to the best of our knowledge, the first instance of a theorem linking directly the memory of the asset price...
Analytical approximation of the transition density in a local volatility model
We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps.
Antieigenvalue analysis for continuum mechanics, economics, and number theory
My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly...
Applications of simulation methods to barrier options driven by Lévy processes.
Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance
We investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in insurance and finance in an attempt to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the strategy applied or the past values of the portfolio. In this setting, a managed investment portfolio serves simultaneously as the underlying security on which the liability/target...
Arbitrage for simple strategies
Various aspects of arbitrage on finite horizon continuous time markets using simple strategies consisting of a finite number of transactions are studied. Special attention is devoted to transactions without shortselling, in which we are not allowed to borrow assets. The markets without or with proportional transaction costs are considered. Necessary and sufficient conditions for absence of arbitrage are shown.
Arbitrage in markets without shortselling with proportional transaction costs
We consider markets with proportional transaction costs and shortsale restrictions. We give necessary and sufficient conditions for the absence of arbitrage and also estimate the super-replication price.
Are volatility indices in international stock markets forward looking?
Assets/liabilities portfolio immunization as an optimization problem
Asymptotics of riskless profit under selling of discrete time call options
A discrete time model of financial market is considered. In the focus of attention is the guaranteed profit of the investor which arises when the jumps of the stock price are bounded. The limit distribution of the profit as the model becomes closer to the classic model of geometrical Brownian motion is established. It is of interest that the approximating continuous time model does not assume any such profit.