Risk-neutral densities: advanced methods of estimating nonnormal options underlying asset prices and returns

2020 ◽  
Author(s):  
André Santos ◽  
João Guerra
Keyword(s):  
Asset Prices ◽  
Underlying Asset ◽  
Risk Neutral

How Does Investor Sentiment Affect Implied Risk-Neutral Distributions of Call and Put Options?

2015 ◽  
Vol 18 (02) ◽  
pp. 1550010 ◽  
Author(s):  
Wen-Ming Szu ◽  
Yi-Chen Wang ◽  
Wan-Ru Yang
Keyword(s):  
Asset Prices ◽  
Investor Sentiment ◽  
Stock Index ◽  
Option Prices ◽  
Differential Impact ◽  
Underlying Asset ◽  
Put Options ◽  
Put Option ◽  
Risk Neutral ◽  
Skewness And Kurtosis

This paper investigates the characteristics of implied risk-neutral distributions separately derived from Taiwan stock index call and put options prices. Differences in risk-neutral skewness and kurtosis between call and put options indicate deviations from put-call parity. We find that the sentiment effect is significantly related to differences between call and put option prices. Our results suggest the differential impact of investor sentiment and consumer sentiment on call and put option traders' expectations about underlying asset prices. Moreover, rational and irrational sentiment components have different influences on call and put option traders' beliefs.

scholarly journals Tranching, CDS, and Asset Prices: How Financial Innovation Can Cause Bubbles and Crashes

2012 ◽  
Vol 4 (1) ◽  
pp. 190-225 ◽  
Author(s):  
Ana Fostel ◽  
John Geanakoplos
Keyword(s):  
Asset Prices ◽  
Asset Price ◽  
Financial Innovation ◽  
Underlying Asset

We show how the timing of financial innovation might have contributed to the mortgage bubble and then to the crash of 2007–2009. We show why tranching and leverage first raised asset prices and why CDS lowered them afterward. This may seem puzzling, since it implies that creating a derivative tranche in the securitization whose payoffs are identical to the CDS will raise the underlying asset price, while the CDS outside the securitization lowers it. The resolution of the puzzle is that the CDS lowers the value of the underlying asset since it is equivalent to tranching cash. (JEL E32, E44, G01, G12, G13, G21).

scholarly journals Pricing American Options Using a Nonparametric Entropy Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Xisheng Yu ◽  
Li Yang
Keyword(s):  
Monte Carlo ◽  
Comparative Analysis ◽  
Least Squares ◽  
American Options ◽  
Monte Carlo Algorithm ◽  
Underlying Asset ◽  
Asset Return ◽  
Pricing Errors ◽  
Risk Neutral ◽  
Pricing Measure

This paper studies the pricing problem of American options using a nonparametric entropy approach. First, we derive a general expression for recovering the risk-neutral moments of underlying asset return and then incorporate them into the maximum entropy framework as constraints. Second, by solving this constrained entropy problem, we obtain a discrete risk-neutral (martingale) distribution as the unique pricing measure. Third, the optimal exercise strategies are achieved via the least-squares Monte Carlo algorithm and consequently the pricing algorithm of American options is obtained. Finally, we conduct the comparative analysis based on simulations and IBM option contracts. The results demonstrate that this nonparametric entropy approach yields reasonably accurate prices for American options and produces smaller pricing errors compared to other competing methods.

ESTIMATING THE PARAMETER DELTA IN THE BLACK MODEL USING THE FINITE DIFFERENCE METHOD FOR FUTURES OPTIONS

2015 ◽  
Vol 3 ◽  
pp. 109-114
Author(s):  
Lucia Švábová
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Asset Prices ◽  
Analytical Formula ◽  
Option Price ◽  
Price Changes ◽  
Underlying Asset ◽  
Futures Contract ◽  
The Finite Difference Method

Financial derivatives are a widely used tool for investors to hedge against the risk caused by changes in asset prices in the financial markets. A usual type of hedging derivative is an asset option. In case of unexpected changes in asset prices, in the investment portfolio, the investor will exercise the option to eliminate losses resulting from these changes. Therefore, it is necessary to include the options in the investor´s portfolio in such a ratio that the losses caused by decreasing of assets prices will be covered by profits from those options. Futures option is a type of call or put option to buy or to sell an option contract at a designated strike price. The change in price of the underlying assets or underlying futures contract causes a change in the prices of options themselves. For investor exercising option as a tool for risk insurance, it is important to quantify these changes. The dependence of option price changes, on the underlying asset or futures option price changes, can be expressed by the parameter delta. The value of delta determines the composition of the portfolio to be risk-neutral. The parameter delta is calculated as a derivation of the option price with respect to the price of the underlying asset, if the option price formula exists. But for some types of more complex options, the analytical formula does not exist, so calculation of delta by derivation is not possible. However, it is possible to estimate the value of delta numerically using the principles of the numerical method called “Finite Difference Method.” In the paper the parameter delta for a Futures call option calculated from the analytical formula and estimated from the Finite difference method are compared.

scholarly journals Pricing Product Options and Using Them to Complete Markets for Functions of Two Underlying Asset Prices

2021 ◽  
Vol 14 (8) ◽  
pp. 355
Author(s):  
Dilip B. Madan ◽  
King Wang
Keyword(s):  
Asset Prices ◽  
Characteristic Functions ◽  
Two Dimensional ◽  
Motion Model ◽  
Complete Markets ◽  
Physical Measure ◽  
Underlying Asset ◽  
Differentiable Functions ◽  
Brownian Motion Model ◽  
The Cost

Options paying the product of put and/or call option payouts at different strikes on two underlying assets are observed to synthesize joint densities and replicate differentiable functions of two underlying asset prices. The pricing of such options is undertaken from three perspectives. The first perspective uses a geometric two-dimensional Brownian motion model. The second inverts two-dimensional characteristic functions. The third uses a bootstrapped physical measure to propose a risk charge minimizing hedge using options on the two underlying assets. The options are priced at the cost of the hedge plus the risk charge.

scholarly journals Nonparametric Estimation of Risk-Neutral Distribution via the Empirical Esscher Transform

2018 ◽  
Vol 15 (2) ◽  
pp. 167
Author(s):  
Manoel Pereira ◽  
Alvaro Veiga
Keyword(s):  
Probability Distributions ◽  
Real Data ◽  
Weighted Sum ◽  
Neutral Model ◽  
Esscher Transform ◽  
Physical Measure ◽  
Underlying Asset ◽  
Sample Paths ◽  
Risk Neutral ◽  
Estimation Of Risk

This paper introduces an empirical version of the Esscher transform for nonparametric option pricing. Traditional parametric methods require the formulation of an explicit risk-neutral model and are operational only for a few probability distributions for the returns of the underlying asset. In our proposal, we make only mild assumptions on the price kernel and there is no need for the formulation of the risk-neutral model. First, we simulate sample paths for the returns under the physical measure P. Then, based on the empirical Esscher transform, the sample is reweighted, giving rise to a risk-neutralized sample from which derivative prices can be obtained by a weighted sum of the options’ payoffs in each path. We analyze our proposal in experiments with artificial and real data.

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