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Quantitative Finance Collector is a blog on Quantitative finance analysis, financial engineering methods in mathematical finance focusing on derivative pricing, quantitative trading and quantitative risk management. Random thoughts on financial markets and personal staff are posted at the sub personal blog.

Mar 12
Journal of Econometrics accepts several papers on option pricing, some are quite interesting and represent the recent developments of this field. I list them here just in case you are also interested.

Smile from the Past: A general option pricing framework with multiple volatility and leverage components
In the current literature, the analytical tractability of discrete time option pricing models is guaranteed only for rather specific types of models and pricing kernels. We propose a very general and fully analytical option pricing framework, encompassing a wide class of discrete time models featuring multiple-component structure in both volatility and leverage, and a flexible pricing kernel with multiple risk premia. Although the proposed framework is general enough to include either GARCH-type volatility, Realized Volatility or a combination of the two, in this paper we focus on realized volatility option pricing models by extending the Heterogeneous Autoregressive Gamma (HARG) model of Corsi et al. (2012) to incorporate heterogeneous leverage structures with multiple components, while preserving closed-form solutions for option prices. Applying our analytically tractable asymmetric HARG model to a large sample of S&P 500 index options, we demonstrate its superior ability to price out-of-the-money options compared to existing benchmarks.


Option pricing with non-Gaussian scaling and infinite-state switching volatility
Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on financial assets. Using a recent model for market dynamics which adequately captures the above stylized facts, we derive closed form equations for option pricing, obtaining the Black & Scholes as a special case. By applying our pricing equations to a major equity index option dataset, we show that inclusion of stylized features in financial modeling moves derivative prices about 30% closer to the market values without the need of calibrating models parameters on available derivative prices.

May 10
Stock returns however exhibit nonormal skewness and kurtosis as pointed out by Hull (1993) and Nattenburg (1994). Moreover, the volatility skews are a consequence of the empirical normality assumption violation. For this reason, Corrado and Su (1996) extend the Black-Scholes formula to account for nonnormal skewness and kurtosis in stock returns.

This package calculates the European put and call option prices using the Corrado and Su (1996) model. This method explicitly allows for excess skewness and kurtosis in an expanded Black-Scholes option pricing formula. The approach adapts a Gram-Charlier series expansions of the standard normal density function to yield an option price formula that is the sum of a Black–Scholes option price plus adjustment terms for nonnormal skewness and kurtosis (Corrado and Su, 1997).
For skewness = 0 and kurtosis = 3, the Corrado-Su option prices are equal to the prices obtained using the Black and Scholes (1973) model.

You can download the Matlab code at Corrado and Su (1996) European Option Prices.

Corrado, C.J., and Su T. Skewness and kurtosis in S&P 500 Index returns implied by option prices. Financial Research 19:175–92, 1996.

Corrado, C.J., and Su T. Implied volatility skews and stock return skewness and kurtosis implied by stock option prices. European Journal of Finance 3:73–85, 1997.

Hull, J.C., "Options, Futures, and Other Derivatives", Prentice Hall, 5th edition, 2003.

Luenberger, D.G., "Investment Science", Oxford Press, 1998.
Jun 10
AirXCell is an online R application framework currently supporting a programmable spreadsheet, an R development environment and various financial calculation forms.

A new calculation form has been implemented recently within AirXCell for financial option pricing (option valuation). The option pricer within AirXCell enables the user to compute theoretical option prices. It already offers an extended set of basic and exotic models (about a dozen) than enables the user to price a wide range of option types:

American options,
European options,
Asian options,
Barrier options,
Binary options,
Currency translated options,
Lookback options,
Multiple assets options and
Multiple exercises options

Many more models are being implemented currently and will be added soon to AirXCell. In addition to the option pricing form, there are other forms especially useful in the same context that provides ways to load asset prices, visualize them, compute the theoretical and historical volatility.

This form is very valuable to quantitative researchers or any finance professional who needs to compute theoretical option prices easily and who is looking for a reliable option pricer.

The Option pricing form presents the user with an HTML form enabling her to set up the model with the required parameters values such as the underlying asset price, the strike price, the volatility of the underlying asset, etc.

For instance, the following form is presented to a user requesting the price of an european option using the Generalized Black Scholes model:

Again, there are many more models and option types coming soon as well as other forms for various other kind of calculations, still mostly oriented towards financial calculation.
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May 21
Noise as Information for Illiquidity: We propose a measure of liquidity for the overall financial market by exploiting its connection with the amount of arbitrage capital in the market and observed price deviations in US Treasuries.

The Risk Map: A New Tool for Validating Risk Models: This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.

Deviations from Put-Call Parity and Stock Return Predictability: Deviations from put-call parity contain information about future returns. Using the difference in implied volatility between pairs of call and put options to measure these deviations we find that stocks with relatively expensive calls outperform stocks with relatively expensive puts by 51 basis points per week.

Nassim Taleb on the J.P.Morgan Trading Loss: Nassim Taleb interviewed on the J.P.Morgan Trading Loss (May 2012).
Feb 17
Stochastic Volatility Models and the Pricing of VIX Options:  this paper examines and compares the performance of a variety of continuous-time volatility models in their ability to capture the behavior of the VIX.

Finding the best distribution that fits the data: the title tells, select a best fitted distribution among dozens candidates for a given data series.

No-Hype Options Trading: Myths, Realities, and Strategies That Really Work realistic strategies to consistently generate income every month, while debunking many myths about options trading that tend to lead retail traders astray.

RStudio in the cloud, for dummies: run cloud computing version of R with RStudio, cool!
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