The risk premia embedded in index options Andersen, Torben G.; Fusari, Nicola; Todorov, Viktor
Journal of financial economics,
09/2015, Volume:
117, Issue:
3
Journal Article
Peer reviewed
Open access
We study the dynamic relation between market risks and risk premia using time series of index option surfaces. We find that priced left tail risk cannot be spanned by market volatility (and its ...components) and introduce a new tail factor. This tail factor has no incremental predictive power for future volatility and jump risks, beyond current and past volatility, but is critical in predicting future market equity and variance risk premia. Our findings suggest a wide wedge between the dynamics of market risks and their compensation, which typically displays a far more persistent reaction following market crises.
•General framework for approximating time-changed Markov processes.•Flexible approach, including three Markov chain approximation strategies.•Accommodates time-changed (subordinated) Levy and ...diffusion processes as special cases.•Pricing for American/Bermudan options, European options, and variance swaps.
In this paper, we propose a general approximation framework for the valuation of (path-dependent) options under time-changed Markov processes. The underlying background process is assumed to be a general Markov process, and we consider the case when the stochastic time change is constructed from either discrete or continuous additive functionals of another independent Markov process. We first approximate the underlying Markov process by a continuous time Markov chain (CTMC), and derive the functional equation characterizing the double transforms of the transition matrix of the resulting time-changed CTMC. Then we develop a two-layer approximation scheme by further approximating the driving process in constructing the time change using an independent CTMC. We obtain a single Laplace transform expression. Our framework incorporates existing time-changed Markov models in the literature as special cases, such as the time-changed diffusion process and the time-changed Lévy process. Numerical experiments illustrate the accuracy of our method.
A sequential quadratic programming numerical method is proposed for American option pricing based on the variational inequality formulation. The variational inequality is discretized using the ...θ-method in time and the finite element method in space. The resulting system of algebraic inequalities at each time step is solved through a sequence of box-constrained quadratic programming problems, with the latter being solved by a globally and quadratically convergent, large-scale suitable reflective Newton method. It is proved that the sequence of quadratic programming problems converges with a constant rate under a mild condition on the time step size. The method is general in solving the variational inequalities for the option pricing with many styles of optimal stopping and complex underlying asset models. In particular, swing options and stochastic volatility and jump diffusion models are studied. Numerical examples are presented to confirm the effectiveness of the method.
•A fast sequential quadratic programming method (SQPM) is developed.•The convergence of the SQPM is proved.•The SQPM can solve non-symmetric variational inequalities.•The SQPM is efficient for solving general classes of American and swing options.
This study examines whether the demand for options, as measured by the net buying pressure of index options, explains the implied volatility structure created by options prices. We decompose the ...buying pressure into the direction‐motivated (i.e., delta‐informed) and the volatility‐motivated (i.e., vega‐informed) demand for options. After controlling for options traders' hedging demand, we find that both delta‐ and vega‐informed trading play significant roles in explaining changes in implied volatility. Foreign institutions are more directionally informed in index options trading than their domestic counterparts are. Domestic investors effectively implement volatility trading using put options.
Is there price discovery in equity options? Muravyev, Dmitriy; Pearson, Neil D.; Paul Broussard, John
Journal of financial economics,
02/2013, Volume:
107, Issue:
2
Journal Article
Peer reviewed
We use tick-by-tick quote data for 39 liquid US stocks and options on them, and we focus on events when the two markets disagree about the stock price in the sense that the option-implied stock price ...obtained from the put-call parity relation is inconsistent with the actual stock price. Option market quotes adjust to eliminate the disagreement, while the stock market quotes behave normally, as if there were no disagreement. The disagreement events are typically precipitated by stock price movements and display signed option volume in the direction that tends to eliminate the disagreements. These results show that option price quotes do not contain economically significant information about future stock prices beyond what is already reflected in current stock prices, i.e., no economically significant price discovery occurs in the option market. We also find no option market price discovery using a much larger sample of disagreement events based on a weaker definition of a disagreement, which verifies that the findings for the primary sample are not due to unusual or unrepresentative market behavior during the put-call parity violations.
The effectiveness of any sanction depends on the costs of avoiding its restrictions. We examine whether bearish option strategies were substitutes for short sales during the September 2008 short-sale ...ban. We find a significant diminution in option volumes and a significant increase in option bid-ask spreads for banned stock relative to unbanned stock during the ban period. Apparent violations of the put-call parity bound became significantly more frequent for banned stocks during the ban period. We conclude that the ban acted as an effective restriction on trading in options.
Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping ...problems, since the dimension corresponds to the number of underlying assets. High-dimensional optimal stopping problems are, however, notoriously difficult to solve due to the well-known curse of dimensionality. In this work, we propose an algorithm for solving such problems, which is based on deep learning and computes, in the context of early exercise option pricing, both approximations of an optimal exercise strategy and the price of the considered option. The proposed algorithm can also be applied to optimal stopping problems that arise in other areas where the underlying stochastic process can be efficiently simulated. We present numerical results for a large number of example problems, which include the pricing of many high-dimensional American and Bermudan options, such as Bermudan max-call options in up to 5000 dimensions. Most of the obtained results are compared to reference values computed by exploiting the specific problem design or, where available, to reference values from the literature. These numerical results suggest that the proposed algorithm is highly effective in the case of many underlyings, in terms of both accuracy and speed.
This paper presents a robust new finding that delta-hedged equity option return decreases monotonically with an increase in the idiosyncratic volatility of the underlying stock. This result cannot be ...explained by standard risk factors. It is distinct from existing anomalies in the stock market or volatility-related option mispricing. It is consistent with market imperfections and constrained financial intermediaries. Dealers charge a higher premium for options on high idiosyncratic volatility stocks due to their higher arbitrage costs. Controlling for limits to arbitrage proxies reduces the strength of the negative relation between delta-hedged option return and idiosyncratic volatility by about 40%.
PDF
