scholarly journals Valuation on an Outside-Reset Option with Multiple Resettable Levels and Dates

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Guangming Xue ◽  
Bin Qin ◽  
Guohe Deng
Keyword(s):  
Risky Asset ◽  
Option Prices ◽  
Strike Price ◽  
Numerical Examples ◽  
External Process ◽  
Reset Option ◽  
Pricing Formula

This paper studies an outside-reset option with multiple strike resets and reset dates, in which the strike price is adjusted by an external process associated with the underlying risky asset. We obtain analytical pricing formula for this option and the hedging parameters Delta and Gamma. Furthermore, some numerical examples are provided to analyze some characteristics of the outside-reset option and to examine the impacts of the external parameters on option prices and Greeks. These results show that the external process can significantly affect option prices and Greeks.

A CLOSED-FORM PRICING FORMULA FOR EUROPEAN EXCHANGE OPTIONS WITH STOCHASTIC VOLATILITY

2021 ◽  
pp. 1-10
Author(s):  
Puneet Pasricha ◽  
Anubha Goel
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stochastic Volatility Model ◽  
Strike Price ◽  
Volatility Model ◽  
Exchange Options ◽  
Pricing Formula ◽  
Exchange Option

This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.

scholarly journals OPTIONS WRITTEN ON STOCKS WITH KNOWN DIVIDENDS

2004 ◽  
Vol 07 (07) ◽  
pp. 901-907
Author(s):  
ERIK EKSTRÖM ◽  
JOHAN TYSK
Keyword(s):  
Stock Price ◽  
Option Price ◽  
Option Prices ◽  
Strike Price ◽  
Call Options ◽  
Alternative Approach ◽  
Black Scholes ◽  
Market Practice ◽  
The Difference ◽  
Risk Free Rate

There are two common methods for pricing European call options on a stock with known dividends. The market practice is to use the Black–Scholes formula with the stock price reduced by the present value of the dividends. An alternative approach is to increase the strike price with the dividends compounded to expiry at the risk-free rate. These methods correspond to different stock price models and thus in general give different option prices. In the present paper we generalize these methods to time- and level-dependent volatilities and to arbitrary contract functions. We show, for convex contract functions and under very general conditions on the volatility, that the method which is market practice gives the lower option price. For call options and some other common contracts we find bounds for the difference between the two prices in the case of constant volatility.

Generalized Analytical Upper Bounds for American Option Prices

2007 ◽  
Vol 42 (1) ◽  
pp. 209-227 ◽  
Author(s):  
San-Lin Chung ◽  
Hsieh-Chung Chang
Keyword(s):  
Interest Rates ◽  
American Options ◽  
General Theorem ◽  
Upper Bounds ◽  
American Option ◽  
Option Prices ◽  
Dividend Yield ◽  
Strike Price ◽  
Risky Assets ◽  
The Interest Rate

AbstractThis paper generalizes and tightens Chen and Yeh's (2002) analytical upper bounds for American options under stochastic interest rates, stochastic volatility, and jumps, where American option prices are difficult to compute with accuracy. We first generalize Theorem 1 of Chen and Yeh (2002) and apply it to derive a tighter upper bound for American calls when the interest rate is greater than the dividend yield. Our upper bounds are not only tight, but also converge to accurate American call option prices when the dividend yield or strike price is small or when volatility is large. We then propose a general theorem that can be applied to derive upper bounds for American options whose payoffs depend on several risky assets. As a demonstration, we utilize our general theorem to derive upper bounds for American exchange options and American maximum options on two risky assets.

scholarly journals The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Naravadee Nualsaard ◽  
Anirut Luadsong ◽  
Nitima Aschariyaphotha
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Basis Functions ◽  
Option Prices ◽  
Time Step ◽  
Numerical Examples ◽  
Black Scholes ◽  
Semiclassical Solution ◽  
Time Linear ◽  
Simple Quadrature

In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process. The approximation of time fractional derivative is interpreted in the Caputo’s sense by a simple quadrature formula. This RBFs approach was theoretically proved with different problems of two numerical examples: time step arbitrage bubble case and time linear arbitrage bubble case. Then, the numerical results were compared with the semiclassical solution in case of fractional order close to 1. As a result, both numerical examples showed that the option prices from RBFs method satisfy the semiclassical solution.

State price density estimation with an application to the recovery theorem

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anthony Sanford
Keyword(s):  
Stock Prices ◽  
Two Dimensions ◽  
Neutral Density ◽  
Option Prices ◽  
Strike Price ◽  
B Splines ◽  
State Price ◽  
Current Estimation ◽  
Risk Neutral ◽  
Risk Neutral Density

Abstract This article introduces a model to estimate the risk-neutral density of stock prices derived from option prices. To estimate a complete risk-neutral density, current estimation techniques use a single mathematical model to interpolate option prices on two dimensions: strike price and time-to-maturity. Instead, this model uses B-splines with at-the-money knots for the strike price interpolation and a mixed lognormal function that depends on the option expiration horizon for the time-to-maturity interpolation. The results of this “hybrid” methodology are significantly better than other risk-neutral density extrapolation methods when applied to the recovery theorem.

On Luhmann's "Soziale System"

2013 ◽  
Vol 16 (1) ◽  
pp. 17-33
Author(s):  
Shuhua Chang ◽  
Wenguang Tang
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Jump Diffusion ◽  
Two Dimensional ◽  
Option Prices ◽  
Pricing Model ◽  
Put Options ◽  
Underlying Process ◽  
Numerical Examples ◽  
Option Pricing Model

AbstractThe purpose of weather option is to allow companies to insure themselves against fluctuations in the weather. However, the valuation of weather option is complex, since the underlying process has no negotiable price. Under the assumption of mean-self-financing, by hedging with a correlated asset which follows a geometric Brownian motion with a jump diffusion process, this paper presents a new weather option pricing model on a stochastic underlying temperature following a mean-reverting Brownian motion. Consequently, a two-dimensional partial differential equation is derived to value the weather option. The numerical method applied in this paper is based on a fitted finite-volume technique combined with the Lagrangian derivative. In addition, the monotonicity, stability, and the convergence of the discrete scheme are also derived. Lastly, some numerical examples are provided to value a series of European HDD-based weather put options, and the effects of some parameters on weather option prices are discussed.

SHORT-TIME IMPLIED VOLATILITY IN EXPONENTIAL LÉVY MODELS

2015 ◽  
Vol 18 (04) ◽  
pp. 1550025
Author(s):  
ERIK EKSTRÖM ◽  
BING LU
Keyword(s):  
Implied Volatility ◽  
Upper And Lower Bounds ◽  
Gaussian Component ◽  
Option Prices ◽  
Strike Price ◽  
Short Time Asymptotics ◽  
Black Scholes ◽  
Exponential Lévy Models ◽  
Necessary And Sufficient ◽  
Short Time

We show that a necessary and sufficient condition for the explosion of implied volatility near expiry in exponential Lévy models is the existence of jumps towards the strike price in the underlying process. When such jumps do not exist, the implied volatility converges to the volatility of the Gaussian component of the underlying Lévy process as the time to maturity tends to zero. These results are proved by comparing the short-time asymptotics of the Black–Scholes price with explicit formulas for upper and lower bounds of option prices in exponential Lévy models.

Currency Target Zones as Mirrored Options

2019 ◽  
Keyword(s):  
Exchange Rate ◽  
Order Approximation ◽  
Lower Boundary ◽  
Option Prices ◽  
Target Zones ◽  
Target Zone ◽  
Strike Price ◽  
The Exchange Rate ◽  
Fundamental Value ◽  
Higher Order Corrections

This article presents a new way of modeling the dynamics of an exchange rate target zone. In the presence of a single upper (lower) target boundary, the exchange rate is precisely represented as the sum of a free float and a short (long) position in a call (put) option with strike price at the boundary. To model a target zone (with two boundaries), a natural approach consists of describing the exchange rate dynamics as the combination of the two, namely the sum of free float together with a long position in a put written on the lower boundary and a short position in a call option written on the upper boundary, respectively. The authors show that this first order approximation leads to significant mispricing (as much as 20%) and must be iterated, leading to an infinite sequence of compounded “mirrored” option prices. They analyze basic properties of such mirrored nested options analytically, describe how to calculate them numerically, and show why it is crucial to take into account higher order corrections in realistic target zones. They argue that this analogy to option prices allows for conceptually simple generalizations that describe different target zone arrangements. They then apply their methodology to the estimation of the fundamental value of the Hong Kong dollar that is hidden by the target zone pegged to the US dollar. They also estimate the implied maturity and explain how this parameter serves as direct proxy for target zone credibility.

scholarly journals Variance Swap Pricing under Markov-Modulated Jump-Diffusion Model

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Shican Liu ◽  
Yu Yang ◽  
Hu Zhang ◽  
Yonghong Wu
Keyword(s):  
Closed Form ◽  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Strike Price ◽  
Transform Method ◽  
Variance Swap ◽  
Continuous Sampling ◽  
Jump Diffusion Model ◽  
Pricing Formula

This paper investigates the pricing of discretely sampled variance swaps under a Markov regime-switching jump-diffusion model. The jump diffusion, as well as other parameters of the underlying stock’s dynamics, is modulated by a Markov chain representing different states of the market. A semi-closed-form pricing formula is derived by applying the generalized Fourier transform method. The counterpart pricing formula for a variance swap with continuous sampling times is also derived and compared with the discrete price to show the improvement of accuracy in our solution. Moreover, a semi-Monte-Carlo simulation is also presented in comparison with the two semi-closed-form pricing formulas. Finally, the effect of incorporating jump and regime switching on the strike price is investigated via numerical analysis.

scholarly journals The Performance of Skewness and Kurtosis Adjusted Option Pricing Model in Emerging Markets

2016 ◽  
Vol 5 (3) ◽  
pp. 70-84
Author(s):  
Özge Sezgin Alp
Keyword(s):  
Emerging Markets ◽  
Option Pricing ◽  
Option Prices ◽  
Pricing Model ◽  
European Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Skewness And Kurtosis ◽  
Pricing Formula

In this study, the option pricing performance of the adjusted Black-Scholes model proposed by Corrado and Su (1996) and corrected by Brown and Robinson (2002), is investigated and compared with original Black Scholes pricing model for the Turkish derivatives market. The data consist of the European options written on BIST 30 index extends from January 02, 2015 to April 24, 2015 for given exercise prices with maturity April 30, 2015. In this period, the strike prices are ranging from 86 to 124. To compare the models, the implied parameters are derived by minimizing the sum of squared deviations between the observed and theoretical option prices. The implied distribution of BIST 30 index does not significantly deviate from normal distribution. In addition, pricing performance of Black Scholes model performs better in most of the time. Black Scholes pricing Formula, Carrado-Su pricing Formula, Implied Parameters

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