18,574 research outputs found
Robust pricing--hedging duality for American options in discrete time financial markets
We investigate pricing-hedging duality for American options in discrete time
financial models where some assets are traded dynamically and others, e.g. a
family of European options, only statically. In the first part of the paper we
consider an abstract setting, which includes the classical case with a fixed
reference probability measure as well as the robust framework with a
non-dominated family of probability measures. Our first insight is that by
considering a (universal) enlargement of the space, we can see American options
as European options and recover the pricing-hedging duality, which may fail in
the original formulation. This may be seen as a weak formulation of the
original problem. Our second insight is that lack of duality is caused by the
lack of dynamic consistency and hence a different enlargement with dynamic
consistency is sufficient to recover duality: it is enough to consider
(fictitious) extensions of the market in which all the assets are traded
dynamically. In the second part of the paper we study two important examples of
robust framework: the setup of Bouchard and Nutz (2015) and the martingale
optimal transport setup of Beiglb\"ock et al. (2013), and show that our general
results apply in both cases and allow us to obtain pricing-hedging duality for
American options.Comment: 29 page
Robust Optimization of Currency Portfolios
We study a currency investment strategy, where we maximize the return on a portfolio of foreign currencies relative to any appreciation of the corresponding foreign exchange rates. Given the uncertainty in the estimation of the future currency values, we employ robust optimization techniques to maximize the return on the portfolio for the worst-case foreign exchange rate scenario. Currency portfolios differ from stock only portfolios in that a triangular relationship exists among foreign exchange rates to avoid arbitrage. Although the inclusion of such a constraint in the model would lead to a nonconvex problem, we show that by choosing appropriate uncertainty sets for the exchange and the cross exchange rates, we obtain a convex model that can be solved efficiently. Alongside robust optimization, an additional guarantee is explored by investing in currency options to cover the eventuality that foreign exchange rates materialize outside the specified uncertainty sets. We present numerical results that show the relationship between the size of the uncertainty sets and the distribution of the investment among currencies and options, and the overall performance of the model in a series of backtesting experiments.robust optimization, portfolio optimization, currency hedging, second-order cone programming
Robust pricing and hedging under trading restrictions and the emergence of local martingale models
We consider the pricing of derivatives in a setting with trading
restrictions, but without any probabilistic assumptions on the underlying
model, in discrete and continuous time. In particular, we assume that European
put or call options are traded at certain maturities, and the forward price
implied by these option prices may be strictly decreasing in time. In discrete
time, when call options are traded, the short-selling restrictions ensure no
arbitrage, and we show that classical duality holds between the smallest
super-replication price and the supremum over expectations of the payoff over
all supermartingale measures. More surprisingly in the case where the only
vanilla options are put options, we show that there is a duality gap. Embedding
the discrete time model into a continuous time setup, we make a connection with
(strict) local-martingale models, and derive framework and results often seen
in the literature on financial bubbles. This connection suggests a certain
natural interpretation of many existing results in the literature on financial
bubbles
Can tests based on option hedging errors correctly identify volatility risk premia?
This paper provides an in-depth analysis of the properties of popular tests for the existence and the sign of the market price of volatility risk. These tests are frequently based on the fact that for some option pricing models under continuous hedging the sign of the market price of volatility risk coincides with the sign of the mean hedging error. Empirically, however, these tests suffer from both discretization error and model mis-specification. We show that these two problems may cause the test to be either no longer able to detect additional priced risk factors or to be unable to identify the sign of their market prices of risk correctly. Our analysis is performed for the model of Black and Scholes (1973) (BS) and the stochastic volatility (SV) model of Heston (1993). In the model of BS, the expected hedging error for a discrete hedge is positive, leading to the wrong conclusion that the stock is not the only priced risk factor. In the model of Heston, the expected hedging error for a hedge in discrete time is positive when the true market price of volatility risk is zero, leading to the wrong conclusion that the market price of volatility risk is positive. If we further introduce model mis-specification by using the BS delta in a Heston world we find that the mean hedging error also depends on the slope of the implied volatility curve and on the equity risk premium. Under parameter scenarios which are similar to those reported in many empirical studies the test statistics tend to be biased upwards. The test often does not detect negative volatility risk premia, or it signals a positive risk premium when it is truly zero. The properties of this test furthermore strongly depend on the location of current volatility relative to its long-term mean, and on the degree of moneyness of the option. As a consequence tests reported in the literature may suffer from the problem that in a time-series framework the researcher cannot draw the hedging errors from the same distribution repeatedly. This implies that there is no guarantee that the empirically computed t-statistic has the assumed distribution. JEL: G12, G13 Keywords: Stochastic Volatility, Volatility Risk Premium, Discretization Error, Model Erro
Preliminary remarks on option pricing and dynamic hedging
An elementary arbitrage principle and the existence of trends in financial
time series, which is based on a theorem published in 1995 by P. Cartier and Y.
Perrin, lead to a new understanding of option pricing and dynamic hedging.
Intricate problems related to violent behaviors of the underlying, like the
existence of jumps, become then quite straightforward by incorporating them
into the trends. Several convincing computer experiments are reported.Comment: 1st International Conference on Systems and Computer Science,
Villeneuve d'Ascq : France (2012
Foreign exchange volatility is priced in equities
This paper finds that standard asset pricing models fail to explain the significantly positive delta hedging errors from writing options on foreign exchange futures. Foreign exchange volatility does influence stock returns, however. The volatility of the JPY/USD exchange rate predicts the time series of stock returns and is priced in the cross-section of stock returns. Foreign exchange volatility risk might be priced because of its relation to foreign exchange level risk. ; Earlier title: Is foreign exchange delta hedging risk priced?Foreign exchange ; Assets (Accounting) ; Prices
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