VALUATION OF COMPOUND OPTION WHEN THE UNDERLYING ASSET IS NON-TRADABLE

2010 ◽  
Vol 13 (03) ◽  
pp. 441-458 ◽  
Author(s):  
YU-HONG LIU
Keyword(s):  
Option Pricing ◽  
Real Options ◽  
Project Investment ◽  
Underlying Asset ◽  
Compound Options

After Geske (1979), compound options — options on options — have been employed in many fields in which real options are applied. The formula for a compound option is convenient to use in real project investment, but it has one drawback — the assets that underlie the compound options are usually non-tradable. This article addresses this issue and proposes two new compound option pricing formulae to overcome this drawback.

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.

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 Good Volatility, Bad Volatility, and Option Pricing

2018 ◽  
Vol 54 (2) ◽  
pp. 695-727 ◽  
Author(s):  
Bruno Feunou ◽  
Cédric Okou
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Asset Price ◽  
Jump Diffusion ◽  
Quadratic Variation ◽  
Pricing Model ◽  
Economic Gain ◽  
Underlying Asset ◽  
Model Free ◽  
Option Pricing Model

Advances in variance analysis permit the splitting of the total quadratic variation of a jump-diffusion process into upside and downside components. Recent studies establish that this decomposition enhances volatility predictions and highlight the upside/downside variance spread as a driver of the asymmetry in stock price distributions. To appraise the economic gain of this decomposition, we design a new and flexible option pricing model in which the underlying asset price exhibits distinct upside and downside semivariance dynamics driven by the model-free proxies of the variances. The new model outperforms common benchmarks, especially the alternative that splits the quadratic variation into diffusive and jump components.

The Condition of the Conditionality

2021 ◽  
Author(s):  
Tumellano Sebehela
Keyword(s):  
Probability Theory ◽  
Option Pricing ◽  
Simultaneous Occurrence ◽  
Option Value ◽  
Hedging Strategy ◽  
Compound Options ◽  
Exotic Option ◽  
Exchange Options ◽  
Nikodym Derivative ◽  
Exchange Option

The interdependence of options is common among compound options. Moreover, this interconnectedness is synonymous with probability theory-how a set of axioms are treated. The conditionality, where one option value is dependent on another option, has spilled over to option pricing, especially exchange options. However, it seems that no study has explored whether that simultaneous occurrence of two options is conditional or not. This study uses conditional approaches (Radon–Nikodým derivative and probability theory) to illustrate conditionality in an exchange option. Furthermore, hedging strategy is derived based on straddles. The results show that due to conditionality another exotic option, tri-conditional option (also known as triple option) is derived. The hedging of a triple option encompasses both dynamic and static techniques.

scholarly journals The European Vulnerable Option Pricing with Jumps Based on a Mixed Model

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Chao Wang ◽  
Jianmin He ◽  
Shouwei Li
Keyword(s):  
Option Pricing ◽  
Mixed Model ◽  
Structural Model ◽  
Jump Diffusion ◽  
Reduced Form ◽  
Martingale Method ◽  
Underlying Asset ◽  
Form Model ◽  
Reduced Form Model ◽  
Vulnerable Option

In this paper, we combine the reduced-form model with the structural model to discuss the European vulnerable option pricing. We define that the default occurs when the default process jumps or the corporate goes bankrupt. Assuming that the underlying asset follows the jump-diffusion process and the default follows the Vasicek model, we can have the expression of European vulnerable option. Then we use the measure transformation and martingale method to derive the explicit solution of it.

Short maturity options for Azéma–Yor martingales

2015 ◽  
Vol 02 (04) ◽  
pp. 1550052
Author(s):  
Lingjiong Zhu
Keyword(s):  
Option Pricing ◽  
Continuous Time ◽  
Time Averaging ◽  
European Options ◽  
Underlying Asset ◽  
Rigorous Study

A class of positive Azéma–Yor martingales was first introduced in the option pricing context by Peter Carr (2014). In this paper, we present a rigorous study of the short maturity asymptotics for Asian, upper barrier, lower barrier and European options with continuous-time averaging, under the assumption that the underlying asset follows a Azéma–Yor martingale.

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