scholarly journals It Takes Two to Tango: Estimation of the Zero-Risk Premium Strike of a Call Option via Joint Physical and Pricing Density Modeling

Risks ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 196
Author(s):  
Stephan Höcht ◽  
Dilip B. Madan ◽  
Wim Schoutens ◽  
Eva Verschueren
Keyword(s):  
Risk Premium ◽  
Pricing Strategy ◽  
Call Option ◽  
Option Prices ◽  
Pricing Model ◽  
Stable Pattern ◽  
European Call Option ◽  
Pricing Measure ◽  
The Stability ◽  
Density Modeling

It is generally said that out-of-the-money call options are expensive and one can ask the question from which moneyness level this is the case. Expensive actually means that the price one pays for the option is more than the discounted average payoff one receives. If so, the option bears a negative risk premium. The objective of this paper is to investigate the zero-risk premium moneyness level of a European call option, i.e., the strike where expectations on the option’s payoff in both the P- and Q-world are equal. To fully exploit the insights of the option market we deploy the Tilted Bilateral Gamma pricing model to jointly estimate the physical and pricing measure from option prices. We illustrate the proposed pricing strategy on the option surface of stock indices, assessing the stability and position of the zero-risk premium strike of a European call option. With small fluctuations around a slightly in-the-money level, on average, the zero-risk premium strike appears to follow a rather stable pattern over time.

Dynamic Robust Pricing Model of European Call Option under the Fractional Market with Knightian Uncertainty

2011 ◽  
Vol 271-273 ◽  
pp. 675-678
Author(s):  
Hui Zhang ◽  
Wen Yu Meng
Keyword(s):  
Financial Market ◽  
Conditional Expectation ◽  
Explicit Solution ◽  
Knightian Uncertainty ◽  
Call Option ◽  
Pricing Model ◽  
European Call Option

The fractional financial market with Knightian uncertainty is studied. Using the important theories of the quasi conditional expectation and the quasi martingale, we establish the dynamic robust pricing model of European call option and get the explicit solution of the model.

scholarly journals Analytical Solution of Black-Scholes Equation in Predicting Market Prices and Its Pricing Bias

2020 ◽  
pp. 17-23
Author(s):  
Azor, Promise Andaowei ◽  
Amadi, Innocent Uchenna
Keyword(s):  
Analytical Solution ◽  
Goodness Of Fit ◽  
Call Option ◽  
Option Prices ◽  
Goodness Of Fit Test ◽  
Market Prices ◽  
European Call Option ◽  
Black Scholes

This paper is geared towards implementation of Black-Scholes equation in valuation of European call option and predicting market prices for option traders. First, we explained how Black-Scholes equation can be used to estimate option prices and then we also estimated the BS pricing bias from where market prices were predicted. From the results, it was discovered that Black-Scholes values were relatively close to market prices but a little increase in strike prices (K) decreases the option prices. Furthermore, goodness of fit test was done using Kolmogorov –Sminorvov to study BSM and Market prices.

scholarly journals Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

2018 ◽  
Vol 10 (6) ◽  
pp. 108
Author(s):  
Yao Elikem Ayekple ◽  
Charles Kofi Tetteh ◽  
Prince Kwaku Fefemwole
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Call Option ◽  
Option Prices ◽  
Options Market ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Real Market ◽  
Independent Path

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

Pricing options on a mean-reverting asset by the analytical operator splitting method

2021 ◽  
pp. 2150002
Author(s):  
C. F. Lo ◽  
Y. W. He
Keyword(s):  
Operator Splitting ◽  
Splitting Method ◽  
Dynamical Symmetry ◽  
Call Option ◽  
Option Prices ◽  
Pricing Options ◽  
Operator Splitting Method ◽  
European Call Option ◽  
Price Formula ◽  
Black Scholes

In this paper, we propose an operator splitting method to valuate options on the inhomogeneous geometric Brownian motion. By exploiting the approximate dynamical symmetry of the pricing equation, we derive a simple closed-form approximate price formula for a European call option which resembles closely the Black–Scholes price formula for a European vanilla call option. Numerical tests show that the proposed method is able to provide very accurate estimates and tight bounds of the exact option prices. The method is very efficient and robust as well.

Dynamic Robust Pricing Model of European Call Option and Empirical Research in Fractional Market

2011 ◽  
Vol 368-373 ◽  
pp. 3226-3229
Author(s):  
Hui Zhang ◽  
Wen Yu Meng
Keyword(s):  
Empirical Research ◽  
Financial Market ◽  
Conditional Expectation ◽  
Explicit Solution ◽  
Knightian Uncertainty ◽  
Call Option ◽  
Pricing Model ◽  
European Call Option

The fractional financial market with Knightian uncertainty is studied. We get the dynamic robust pricing model of European call option. Using the important theories of the quasi conditional expectation and the quasi martingale, we get the explicit solution of the model. By making empirical research on the financial product of Chinese bank ahead 09004, we depict the important impacts of the Knightian uncertainty on the robust pricing of European call option.

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