Option pricing

Security prices contain valuable information that can be used to make a wide variety of economic decisions. To extract this information, a model is required that relates market prices to the desired information, and that ideally can be implemented using timely and low-cost methods. The authors explore two models applied to option prices to extract the risk-neutral probability density function (R-PDF) of the expected Can$/US$ exchange rate. Each of the two models extends the Black-Scholes model by using a mixture of two lognormals for the terminal distribution, instead of a single lognormal: one mixed lognormal imposes a specific stochastic process for the underlying asset, and the other does not. The contribution of the paper is to propose a simple methodology to build R-PDFs with a constant time to maturity in the absence of option prices for the maturity of interest. The authors apply this methodology and find that the two models provide similar results for the degree of uncertain...

Robust calibration of option valuation models to quoted option prices is non-trivial but crucial for good performance. A framework based on the state-space formulation of the option valuation model is introduced. Non-linear (Kalman) filters are needed to do inference since the models have latent variables (e.g. volatility). The statistical framework is made adaptive by introducing stochastic dynamics for the parameters. This allows the parameters to change over time, while treating the measurement noise in a statistically consistent way and using all data efficiently. The performance and computational efficiency of standard and iterated extended Kalman filters (EKF and IEKF) are investigated. These methods are compared to common calibration such as weighted least squares (WLS) and penalized weighted least squares (PWLS). A simulation study, using the Bates model, shows that the adaptive framework is capable of tracking time varying parameters and latent processes such as stochastic ...

The master thesis studies the applicability of Black-Scholes-Model extensions to pricing options on stock indices. Polish options on the WIG20 stock index traded on the GPW the provide for the object of the study. The thesis analyses the characteristics of the Polish derivative market and applies stochastic theory to pricing Polish options. The traditional Black-Scholes-Merton model is extended to accommodate various stochastic approaches including Martingale Pricing methods, Fourier Transforms, and Monte-Carlo simulation. The approaches are implemented by means of the Python computer language. The results produced by different pricing methods are compared to the results of the standard Black-Scholes-Merton.

[the download only contains excerpts, but you are welcome to contact me for more info]

The main contribution of the paper is to present hard evidence on risk exposure, hedging strategies, and agency problems resulting in speculation with derivatives, by focusing on the case of Aracruz Celulose. It highlights the failure of risk management systems in non-financial firms in the face of extreme events like the financial crisis of 2008. The company posted financial losses of U$2.1 billion due to currency derivatives trading in the third quarter of 2008. We show how the company‟s real hedge position deviated from its optimal hedge as a result of the speculation with OTC derivatives, permitted by weak governance structures that failed in preventing hubris and mistakes in risk management.

The adoption of copula functions is suggested in order to price bivariate contingent claims. Copulas enable the marginal distributions extracted from vertical spreads in the options markets to be imbedded in a multivariate pricing kernel. It is proved that such a kernel is a copula function, and that its super-replication strategy is represented by the Frechet bounds. Applications provided include

What means pricing? It is a method adopted by a firm to set its selling price. Pricing methods are the combination of different marketing decision variables being used by the firm to market its goods. Good's price is an important factor in determining its market demand. Pricing should be aimed toward a goal. Pricing methods is a greatest strategy for attaining competitive advantage for any firm. Price is one of the most important variables in the marketing mix. Its importance has increased substantially over the years because of environmental factors like recession, intensity of inter firm rivalry, and the customer becoming aware of alternatives. In order to arrive at the mot acceptable price level, the marketer needs the information on customers, competition, and the firm's cost structure. This is only possible by an accurate blend of all the elements pricing strategy as it helps in achieving organizational goals of profit maximization by high sales volume, attaining higher market share and satisfied customers. O que significa precificação? É um procedimento adotado pelas empresas para determinação dos seus preços de venda. A precificação é uma a combinação de diferentes variáveis de decisão de marketing a ser usado pela usado pela empresa para comercializar suas mercadorias. O preço das mercadorias é um fator importante para determinar a demanda do mercado. O preço deve ser direcionado para uma meta. A precificação é a maior estratégia para a obtenção de vantagem competitiva para qualquer empresa. O preço é uma das variáveis mais importantes no marketing mix. Sua importância aumentou substancialmente ao longo dos anos por causa de fatores ambientais como recessão, intensidade de rivalidade entre empresas e a própria consciência do cliente em tomar alternativas. Para chegar ao nível de preço aceitável, a empresa precisa das informações sobre os clientes, da concorrência e da estrutura de custos da empresa. Isso só é possível através de um " mix " preciso de todos os elementos estratégia de preços, uma vez que ajuda na realização de objetivos organizacionais de maximização do lucro por volume de vendas, atingindo maior quota de mercado e clientes satisfeitos.

The Black-Scholes model is used by investors and traders to price and hedge different types of derivatives and was originally developed early in the 1970s by Fischer Black, Myron Scholes and Robert Merton (Hull, 2012). There exist a variety of different versions and extensions of the model specially designed to analyse specific relations and derivatives. Even though there are some key differences between the different versions of the model, they have in common that they all assume no arbitrage. In this essay the two ways in which the Black-Scholes pricing relationship relies on the no arbitrage assumption will be discussed by going through a simple delta hedging derivation of the model. The differences between the two no arbitrage conditions, regarding information and market behaviour, will then be discussed and be related to actual observations in financial markets

We build a heuristic that takes a given option price in the tails with strike K and extends (for calls, all strikes > K, for put all strikes < K) assuming the continuation falls into what we define as "Karamata Constant" over which the strong Pareto law holds. The heuristic produces relative prices for options, with for sole parameter the tail index α under some mild arbitrage constraints.
Usual restrictions such as finiteness of variance are not required.
The heuristic allows us to scrutinize the volatility surface and test theories of tail option mispricing and overpricing usually built on thin tailed models and modification of the Black-Scholes formula.

The ability to forecast the volatility of the markets is critical to analysts. Among the large array of approaches available for forecasting volatility, neural networks are gaining in popularity. We present a primer for using neural networks for financial forecasting. We compare volatility forecasts from neural networks with implied volatility from S&P 500 Index futures options using the Barone-Adesi and Whaley (BAW) American futures options pricing model. Forecasts from neural networks outperform implied volatility forecasts and are not found to be significantly different from realized volatility. Implied volatility forecasts are found to be significantly different from realized volatility in two of three forecast horizons.

Research paper that lists the sukuk issuance where default event took place
====

Estimating Investor Losses in Sukuk Default Restructuring (Universiti Sains Islam Malaysia)

"The aim of the study is to estimate investor losses in case of sukuk default restructuring using government and corporate sukuk as a benchmark. The main findings suggest that the average investor losses ranging from 2.01% - 3.14% (for less than or equal to 1 year remaining tenure) to 18.15% - 18.94% (for more than 5 years remaining tenure). The findings indicate that investors will face relatively bigger losses if the defaulted sukuk have longer remaining tenure. This finding may be used by market participants as benchmark in restructuring process" 

A study conducted by Khnifer (2010a) is one of the early studies that discuss the sukuk default. In his paper, the author reports that there are at least 21 defaulted sukuk in last 20 months from Nov. 2010. Khnifer (2010b) further proposes three approaches to restructure defaulted sukuk based on Shari’ah principles namely haircut, rescheduling and debt-for-equity swaps.

This paper is a rewrite of a former paper comparing the Louis Bachelier option pricing construct and that of Black Scholes Merton option pricing model,
The present paper compares the construct and form of the Black-Scholes Merton (B-SM) and the Louis Bachelier option pricing models in terms of their contemporary markets and contracts, and the underlying pricing construct. To illustrate the comparison the Louis Bachelier model is adapted for features of modern traded option contracts by allowing for the premium's present value form, and incorporating the log-normal and continuous compound assumptions. This demonstrates the B-SM model approximation for the pdf at the boundary point using the differential in the cdf +/-the standard dispersal. This comparison concludes that the Black-Scholes Merton model, and its related precedents and antecedents, are thus approximations and derivative of the Louis Bachelier construct flowing from application of the Fourier heat equation. As part of the analysis the paper reviews critiques of the Bachelier construct in the financial literature; and similarly critiques the modelling and logical construct behind the Black-Scholes Merton model. In particular,

American option pricing is challenging in terms of numerical methods as
they can be exercised anytime. There is a mixture of advantages and disadvantages of particular methods. Binomial trees are simpler, faster but may not approximate any diffusion process and may be difficult to implement for high-dimensional options. On the other hand, Monte Carlo methods are computationally complex due to the large number of iterations involved but can be successfully applied to any diffusion model as well as high-dimensional options. The purpose of this thesis is to assess the efficiency of pricing methods for American and Bermudan style option on several diffusion processes and in both one and two dimensions. The thesis shows that binomial trees give a good
approximation for the Ornstein-Uhlenbeck and CEV processes. Monte Carlo can be applied for American options by approximating the optimal stopping strategy with cross-sectional regression over a set of basis functions yielding lower bound for the true price. Additionally, the upper bound is obtained through a minimization problem over a set of martingales, in a duality setting.

Two different trading accounts were made in Stocktrack.com software trading simulation for the purpose of the Financial derivatives (FD) module. One was ‘buy and hold’ (where you bought FD for three months) the second was ‘trading’ (where you traded different FD on daily basis). On both we had to write reports of what methods – approaches we used on trading and choosing by also writing blog about it.