Search results for "Valuation of options"
showing 10 items of 28 documents
Pricing Sovereign Contingent Convertible Debt
2016
We develop a pricing model for sovereign contingent convertible bonds (S-CoCo) with payment standstills triggered by a sovereign's credit default swap CDS spread. One innovation is the modeling of CDS spread regime switching which is prevalent during crises. Regime switching is modeled as a hidden Markov process and is integrated with a stochastic process of spread levels to obtain S-CoCo prices through simulation. The paper goes a step further and uses the pricing model in a Longstaff-Schwartz. American option pricing framework to compute state contingent S-CoCo prices at some risk horizon, thus facilitating risk management. Dual trigger pricing is also discussed using the idiosyncratic CD…
OPTION VALUE CALCULATION AFFECTED COMPONENTS
2021
As the subprime credit crisis has attracted attention to financial derivative instruments, more frequently arises questions about fairvalue calculations. Over the time, different models had been introduced. All of those models take into account factors affectingprices. Mostly, factors used in calculations on the same type of financial instruments are approximately the same. Therefore questionarises, which factor affects price more and which less, with no matter which model would be used for fair value calculations. One offinancial derivative instrument types is options. Options are agreements, which give to option buyer rights to buy or sell underlyingasset. While the seller or writer of op…
Contingent claim valuation in a market with different interest rates
1995
The problem of contingent claim valuation in a market with a higher interest rate for borrowing than for lending is discussed. We give results which cover especially the European call and put options. The method used is based on transforming the problem to suitable auxiliary markets with only one interest rate for borrowing and lending and is adapted from a paper of Cvitanic and Karatzas (1992) where the authors study constrained portfolio problems.
Operator splitting methods for American option pricing
2004
Abstract We propose operator splitting methods for solving the linear complementarity problems arising from the pricing of American options. The space discretization of the underlying Black-Scholes Scholes equation is done using a central finite-difference scheme. The time discretization as well as the operator splittings are based on the Crank-Nicolson method and the two-step backward differentiation formula. Numerical experiments show that the operator splitting methodology is much more efficient than the projected SOR, while the accuracy of both methods are similar.
On the Irrelevance of Expected Stock Returns in the Pricing of Options in the Binomial Model: A Pedagogical Note
2005
The option pricing theory is now either a standard or a main part of many financial courses on both intermediate and advanced levels. All the textbooks that include the option pricing theory present a detailed treatment of the binomial model. However, the binomial model, although quite simple and intuitive in appearance, is rather tricky when it comes to its practical implementations and applications. In fact, it is amazing that the students often get totally confused when it finally comes to the issue of the choice of the parameters of the binomial model. The reason for all this confusion lies in the fact that all the textbooks emphasize the irrelevance of the binomial option price from th…
TUG-OF-WAR, MARKET MANIPULATION, AND OPTION PRICING
2014
We develop an option pricing model based on a tug-of-war game involving the the issuer and holder of the option. This two-player zero-sum stochastic differential game is formulated in a multi-dimensional financial market and the agents try, respectively, to manipulate/control the drift and the volatility of the asset processes in order to minimize and maximize the expected discounted pay-off defined at the terminal date $T$. We prove that the game has a value and that the value function is the unique viscosity solution to a terminal value problem for a partial differential equation involving the non-linear and completely degenerate parabolic infinity Laplace operator.
Valuation of Barrier Options in a Black-Scholes Setup with Jump Risk
1999
This paper discusses the pitfalls in the pricing of barrier options approximations of the underlying continuous processes via discrete lattice models. These problems are studied first in a Black-Scholes model. Improvements result from a trinomial model and a further modified model where price changes occur at the jump times of a Poisson process. After the numerical difficulties have been resolved in the Black-Scholes model, unpredictable discontinuous price movements are incorporated.
High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation
2001
A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.
Pricing the Option to Surrender in Incomplete Markets
2010
New international accounting standards require insurers to reflect the value of embedded options and guarantees in their products. Pricing techniques based on the Black and Scholes paradigm are often used; however, the hypotheses underneath this model are rarely met. We propose a framework that encompasses the most known sources of incompleteness. We show that the surrender option, joined with a wide range of claims embedded in insurance contracts, can be priced through our tool, and deliver hedging portfolios to mitigate the risk arising from their positions. We provide extensive empirical analysis to highlight the effect of incompleteness on the fair value of the option.
The Random-Time Binomial Model
1999
In this paper we study Binomial Models with random time steps. We explain, how calculating values for European and American Call and Put options is straightforward for the Random-Time Binomial Model. We present the conditions to ensure weak-convergence to the Black-Scholes setup and convergence of the values for European and American put options. Differently to the CRR-model the convergence behaviour is extremely smooth in our model. By using extrapolation we therefore achieve order of convergence two. This way it is an efficient tool for pricing purposes in the Black-Scholes setup, since the CRR model and its extrapolations typically achieve order one. Moreover our model allows in a straig…