37,541 research outputs found
Filtering returns for unspecified biases in priors when testing asset pricing theory
Procedures are presented that allow the empiricist to estimate and test asset pricing models on limited-liability securities without the assumption that the historical payoff distribution provides a consistent estimate of the market's prior beliefs. The procedures effectively filter return data for unspecified historical biases in the market's priors. They do not involve explicit estimation of the market's priors, and hence, economize on parameters. The procedures derive from a new but simple property of Bayesian learning, namely: if the correct likelihood is used, the inverse posterior at the true parameter value forms a martingale process relative to the learner's information filtration augmented with the true parameter value. Application of this central result to tests of asset pricing models requires a deliberate selection bias. Hence, as a by-product, the article establishes that biased samples contain information with which to falsify an asset pricing model or estimate its parameters. These include samples subject to, e.g. survivorship bias or Peso problems
Option Pricing using Quantum Computers
We present a methodology to price options and portfolios of options on a
gate-based quantum computer using amplitude estimation, an algorithm which
provides a quadratic speedup compared to classical Monte Carlo methods. The
options that we cover include vanilla options, multi-asset options and
path-dependent options such as barrier options. We put an emphasis on the
implementation of the quantum circuits required to build the input states and
operators needed by amplitude estimation to price the different option types.
Additionally, we show simulation results to highlight how the circuits that we
implement price the different option contracts. Finally, we examine the
performance of option pricing circuits on quantum hardware using the IBM Q
Tokyo quantum device. We employ a simple, yet effective, error mitigation
scheme that allows us to significantly reduce the errors arising from noisy
two-qubit gates.Comment: Fixed a typo. This article has been accepted in Quantu
Empirical pricing kernels obtained from the UK index options market
Empirical pricing kernels for the UK equity market are derived as the ratio between risk-neutral densities, inferred from FTSE 100 index options, and historical real-world densities, estimated from time series of the index. The kernels thus obtained are almost compatible with a risk averse representative agent, unlike similar estimates for the US market
Non-Parametric Extraction of Implied Asset Price Distributions
Extracting the risk neutral density (RND) function from option prices is well
defined in principle, but is very sensitive to errors in practice. For risk
management, knowledge of the entire RND provides more information for
Value-at-Risk (VaR) calculations than implied volatility alone [1]. Typically,
RNDs are deduced from option prices by making a distributional assumption, or
relying on implied volatility [2]. We present a fully non-parametric method for
extracting RNDs from observed option prices. The aim is to obtain a continuous,
smooth, monotonic, and convex pricing function that is twice differentiable.
Thus, irregularities such as negative probabilities that afflict many existing
RND estimation techniques are reduced. Our method employs neural networks to
obtain a smoothed pricing function, and a central finite difference
approximation to the second derivative to extract the required gradients.
This novel technique was successfully applied to a large set of FTSE 100
daily European exercise (ESX) put options data and as an Ansatz to the
corresponding set of American exercise (SEI) put options. The results of paired
t-tests showed significant differences between RNDs extracted from ESX and SEI
option data, reflecting the distorting impact of early exercise possibility for
the latter. In particular, the results for skewness and kurtosis suggested
different shapes for the RNDs implied by the two types of put options. However,
both ESX and SEI data gave an unbiased estimate of the realised FTSE 100
closing prices on the options' expiration date. We confirmed that estimates of
volatility from the RNDs of both types of option were biased estimates of the
realised volatility at expiration, but less so than the LIFFE tabulated
at-the-money implied volatility.Comment: Paper based on Application of Physics in Financial Analysis,APFA5,
Conference Presentation, Torino, Italy. 11.5 Page
On an optimization problem related to static super-replicating strategies
In this paper, we investigate an optimization problem related to super-replicating strategies for European-type call options written on a weighted sum of asset prices, following the initial approach in Chen et al. (2008). Three issues are investigated. The first issue is the (non-)uniqueness of the optimal solution. The second issue is the generalization to an optimization problem where the weights may be random. This theory is then applied to static super-replication strategies for some exotic options in a stochastic interest rate setting. The third issue is the study of the co-existence of the comonotonicity property and the martingale property.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Vanna-Volga methods applied to FX derivatives : from theory to market practice
We study Vanna-Volga methods which are used to price first generation exotic
options in the Foreign Exchange market. They are based on a rescaling of the
correction to the Black-Scholes price through the so-called `probability of
survival' and the `expected first exit time'. Since the methods rely heavily on
the appropriate treatment of market data we also provide a summary of the
relevant conventions. We offer a justification of the core technique for the
case of vanilla options and show how to adapt it to the pricing of exotic
options. Our results are compared to a large collection of indicative market
prices and to more sophisticated models. Finally we propose a simple
calibration method based on one-touch prices that allows the Vanna-Volga
results to be in line with our pool of market data
- …