C omplex derivatives have become accepted instruments to tailor risk coverage for risk managers and investors. Barrier-type options have become important instruments, particularly for the valuation of structured products (see Banks [1994]). They are also widely used in currency markets. The holder of a barrier option acquires option coverage on only a subset of the risky outcomes for which a pl...

We demonstrate that including continuous and discrete tunnel barrier height distributions in otherwise traditional tunneling formalisms enables straightforward modeling of several phenomena important to tunneling. Random barrier height inhomogeneities significantly impact the tunneling conductance, as evidenced by ideal tunneling models extracting faulty barrier parameters, with the incurred er...

We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in barrier options under the Heston (1993) stochastic volatility model. This is done by modifying the LT method from Imai and Tan (2006) for the Heston model such that the first uniform variable does not influence the stochastic volatility path and then conditionally modifying its marginals to fulfill the barrier condition...

Pricing financial options often requires Monte Carlo methods. One particular case is that of barrier options, whose payoff may be zero depending on whether or not an underlying asset crosses a barrier during the life of the option. This paper develops variance reduction techniques that take advantage of the special structure of barrier options, and are appropriate for general simulation problem...

The purpose of this thesis is to investigate the pricing of financial options under the 2-hypergeometricstochastic volatility model. This is an analytically tractable model which has recently been introducedas an attempt to tackle one of the most serious shortcomings of the famous Black and Scholes optionpricing model: the fact that it does not reproduce the volatility smile and ske...

Barrier options are a widely used class of path-dependent derivative securities. These options either cease to exist or come into existence when some pre-specified asset price barrier is hit during the option’s life. Merton (1973) has derived a down-and-out call price by solving the corresponding partial differential equation with some boundary conditions. Reiner & Rubinstein (1991) published c...

In this paper, we construct a numerical method to the solution of Black-Scholes partial differential equation modelling Barrier option pricing problem on a single asset. We use finite difference approximations for temporal derivative and then the option price is approximated with the redefined B-spline functions. Stability of this method has been discussed and shown that it is unconditionally s...

The purpose of this project is to extend the Heston model in order to incorporate the term structure (TS) of the implied volatility surface. This includes implementing a TS within the Heston model and its calibration to a set of market instruments. The TS Heston model with piecewise constant parameters is implemented to match the TS and the COS pricing method is used for fast option pricing. We...

A barrier option is a derivative contract that is activated or extinguished when the price of the underlying asset crosses a certain level. Most models assume continuous monitoring of the barrier. However, in practice, most, if not all, of the barrier options traded are discretely monitored. Unlike their continuous counterparts, there is essentially no closed form solution available, and even n...