scholarly journals Additive logistic processes in option pricing

2021 ◽  
Author(s):  
Peter Carr ◽  
Lorenzo Torricelli
Keyword(s):  
Option Pricing ◽  
Pricing Models ◽  
Underlying Asset ◽  
Formula One ◽  
Additive Type ◽  
Black Scholes ◽  
Minimum Price ◽  
Risk Neutral ◽  
Risk Neutral Probabilities ◽  
Security Price

AbstractIn option pricing, it is customary to first specify a stochastic underlying model and then extract valuation equations from it. However, it is possible to reverse this paradigm: starting from an arbitrage-free option valuation formula, one could derive a family of risk-neutral probabilities and a corresponding risk-neutral underlying asset process. In this paper, we start from two simple arbitrage-free valuation equations, inspired by the log-sum-exponential function and an $\ell ^{p}$ ℓ p vector norm. Such expressions lead respectively to logistic and Dagum (or “log-skew-logistic”) risk-neutral distributions for the underlying security price. We proceed to exhibit supporting martingale processes of additive type for underlying securities having as time marginals two such distributions. By construction, these processes produce closed-form valuation equations which are even simpler than those of the Bachelier and Samuelson–Black–Scholes models. Additive logistic processes provide parsimonious and simple option pricing models capturing various important stylised facts at the minimum price of a single market observable input.

Value-at-Risk and Expected Shortfall approaches for option premiums and the probability of default estimation based on ARMA models

2021 ◽  
Vol 57 (3) ◽  
pp. 126
Author(s):  
Nikolai Berzon
Keyword(s):  
Time Series ◽  
Option Pricing ◽  
Discrete Time ◽  
Value At Risk ◽  
Probability Of Default ◽  
Pricing Models ◽  
Arma Process ◽  
Underlying Asset ◽  
Black Scholes

The need to address the issue of risk management has given rise to a number of models for estimation the probability of default, as well as a special tool that allows to sell credit risk – a credit default swap (CDS). From the moment it appeared in 1994 until the crisis of 2008, that the CDS market was actively growing, and then sharply contracted. Currently, there is practically no CDS market in emerging economies (including Russia). This article is to improve the existing CDS valuation models by using discrete-time models that allow for more accurate assessment and forecasting of the selected asset dynamics, as well as new option pricing models that take into account the degree of risk acceptance by the option seller. This article is devoted to parametric discrete-time option pricing models that provide more accurate results than the traditional Black-Scholes continuous-time model. Improvement in the quality of assessment is achieved due to three factors: a more detailed consideration of the properties of the time series of the underlying asset (in particular, autocorrelation and heavy tails), the choice of the optimal number of parameters and the use of Value-at-Risk approach. As a result of the study, expressions were obtained for the premiums of European put and call options for a given level of risk under the assumption that the return on the underlying asset follows a stationary ARMA process with normal or Student's errors, as well as an expression for the credit spread under similar assumptions. The simplicity of the ARMA process underlying the model is a compromise between the complexity of model calibration and the quality of describing the dynamics of assets in the stock market. This approach allows to take into account both discreteness in asset pricing and take into account the current structure and the presence of interconnections for the time series of the asset under consideration (as opposed to the Black–Scholes model), which potentially allows better portfolio management in the stock market.

LOCALLY RISK-NEUTRAL VALUATION OF OPTIONS IN GARCH MODELS BASED ON VARIANCE-GAMMA PROCESS

2012 ◽  
Vol 15 (02) ◽  
pp. 1250015 ◽  
Author(s):  
LIE-JANE KAO
Keyword(s):  
Option Pricing ◽  
Sufficient Conditions ◽  
Garch Model ◽  
Gamma Process ◽  
Type Model ◽  
Underlying Asset ◽  
Variance Gamma ◽  
Variance Gamma Process ◽  
Black Scholes ◽  
Risk Neutral

This study develops a GARCH-type model, i.e., the variance-gamma GARCH (VG GARCH) model, based on the two major strands of option pricing literature. The first strand of the literature uses the variance-gamma process, a time-changed Brownian motion, to model the underlying asset price process such that the possible skewness and excess kurtosis on the distributions of asset returns are considered. The second strand of the literature considers the propagation of the previously arrived news by including the feedback and leverage effects on price movement volatility in a GARCH framework. The proposed VG GARCH model is shown to obey a locally risk-neutral valuation relationship (LRNVR) under the sufficient conditions postulated by Duan (1995). This new model provides a unified framework for estimating the historical and risk-neutral distributions, and thus facilitates option pricing calibration using historical underlying asset prices. An empirical study is performed comparing the proposed VG GARCH model with four competing pricing models: benchmark Black–Scholes, ad hoc Black–Scholes, normal NGARCH, and stochastic volatility VG. The performance of the VG GARCH model versus these four competing models is then demonstrated.

scholarly journals Quanto Pricing beyond Black–Scholes

2021 ◽  
Vol 14 (3) ◽  
pp. 136
Author(s):  
Holger Fink ◽  
Stefan Mittnik
Keyword(s):  
Option Pricing ◽  
Goodness Of Fit ◽  
Calibration Procedure ◽  
Barrier Options ◽  
Pricing Models ◽  
Modeling Framework ◽  
Double Barrier ◽  
Parameter Stability ◽  
Comprehensive Data ◽  
Black Scholes

Since their introduction, quanto options have steadily gained popularity. Matching Black–Scholes-type pricing models and, more recently, a fat-tailed, normal tempered stable variant have been established. The objective here is to empirically assess the adequacy of quanto-option pricing models. The validation of quanto-pricing models has been a challenge so far, due to the lack of comprehensive data records of exchange-traded quanto transactions. To overcome this, we make use of exchange-traded structured products. After deriving prices for composite options in the existing modeling framework, we propose a new calibration procedure, carry out extensive analyses of parameter stability and assess the goodness of fit for plain vanilla and exotic double-barrier options.

scholarly journals Reverse Bonus Certificate Design and Valuation Using Pricing by Duplication Methods

2015 ◽  
Vol 62 (3) ◽  
pp. 277-289
Author(s):  
Martina Bobriková ◽  
Monika Harčariková
Keyword(s):  
Option Pricing ◽  
Exotic Options ◽  
Pricing Models ◽  
Underlying Asset ◽  
Replication Method ◽  
Maturity Date ◽  
Derivative Market ◽  
Replicating Portfolio ◽  
Pricing Formula

Abstract In this paper we perform an analysis of a capped reverse bonus certificate, the value of which is derived from the value of an underlying asset. A pricing formula for the portfolio replication method is applied to price the capped reverse bonus certificate. A replicating portfolio has profit that is identical to profit from a combination of positions in spot and derivative market, i.e. vanilla and exotic options. Based upon the theoretical option pricing models, the replicating portfolio for capped reverse bonus certificate on the Euro Stoxx 50 index is engineered. We design the capped reverse bonus certificate with various parameters and calculate the issue prices in the primary market. The profitability for the potential investor at the maturity date is provided. The relation between the profit change of the investor and parameters’ change is detected. The best capped reverse bonus certificate for every estimated development of the index is identified.

scholarly journals Risk‐neutral moment‐based estimation of affine option pricing models

2018 ◽  
Vol 33 (7) ◽  
pp. 1007-1025 ◽  
Author(s):  
Bruno Feunou ◽  
Cédric Okou
Keyword(s):  
Option Pricing ◽  
Pricing Models ◽  
Risk Neutral

scholarly journals Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

2016 ◽  
Vol 8 (3) ◽  
pp. 123
Author(s):  
Aparna Bhat ◽  
Kirti Arekar
Keyword(s):  
Option Pricing ◽  
Closed Form Solution ◽  
Time Varying ◽  
Pricing Model ◽  
Currency Options ◽  
Pricing Models ◽  
Pricing Options ◽  
Volatility Model ◽  
Black Scholes ◽  
Option Pricing Model

Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models – the Black-Scholes-Merton Option Pricing Model (BSM) and Duan’s NGARCH option pricing model – for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the ‘volatility smile’. This bias of the BSM results from its assumption of a constant volatility over the option’s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

scholarly journals Option Pricing Based on Modified Advection-Dispersion Equation: Stochastic Representation and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Longjin Lv ◽  
Luna Wang
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Dispersion Equation ◽  
Mean Square Displacement ◽  
Mean Square ◽  
European Option ◽  
Stochastic Representation ◽  
Pricing Models ◽  
Advection Dispersion ◽  
Black Scholes

In this paper, we first investigate the stochastic representation of the modified advection-dispersion equation, which is proved to be a subordinated stochastic process. Taking advantage of this result, we get the analytical solution and mean square displacement for the equation. Then, applying the subordinated Brownian motion into the option pricing problem, we obtain the closed-form pricing formula for the European option, when the underlying of the option contract is supposed to be driven by the subordinated geometric Brownian motion. At last, we compare the obtained option pricing models with the classical Black–Scholes ones.

Option pricing models

1989 ◽  
Vol 116 (3) ◽  
pp. 537-558 ◽  
Author(s):  
D. Blake
Keyword(s):  
Option Pricing ◽  
Binomial Model ◽  
Pricing Models ◽  
Black Scholes Model ◽  
Black Scholes

ABSTRACTThe paper discusses two important models of option pricing: the binomial model and the Black—Scholes model. It begins with a brief description of options.

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