American options with acceleration clauses

Acceleration clauses shorten the residual life of an option when an acceleration condition is met. Acceleration clauses are frequent in warrants, American call options on traded stocks. In warrants with the acceleration clause, if an index (e.g. the average underlying stock) triggers an acceleration threshold, the American call option can be exercised on a much shorter maturity (e.g. 30 days). The actual time-to-maturity of an American option with an acceleration condition is therefore stochastic. In order to evaluate these contracts we first reduce the generic American option with stochastic time-to-maturity to a compound American option with constant maturity, and provide estimates for their prices. Finally we propose an efficient algorithm to price American call options with the acceleration clause in a binomial setting

The put-call symmetry for American options in the Heston stochastic volatility model

We extend to the Heston stochastic volatility framework the parity result of McDonald and Schroder (1998) for American call and put options

Optimal exercise of American put options near maturity: A new economic perspective

The critical price S 17(t) of an American put option is the underlying stock price level that triggers its immediate optimal exercise. We provide a new perspective on the determination of the critical price near the option maturity T when the jump-adjusted dividend yield of the underlying stock is either greater than or weakly smaller than the riskfree rate. Firstly, we prove that S 17(t) coincides with the critical price of the covered American put (a portfolio that is long in the put as well as in the stock). Secondly, we show that the stock price that represents the indifference point between exercising the covered put and waiting until T is the European-put critical price, at which the European put is worth its intrinsic value. Finally, we prove that the indifference point\u2019s behavior at T equals S 17(t)\u2019s behavior at T when the stock price is either a geometric Brownian motion or a jump-diffusion. Our results provide a thorough economic analysis of S 17(t) and rigorously show the correspondence of an American option problem to an easier European option problem at maturity

American options and stochastic interest rates

We study finite-maturity American equity options in a stochastic mean-reverting diffusive interest rate framework. We allow for a non-zero correlation between the innovations driving the equity price and the interest rate. Importantly, we also allow for the interest rate to assume negative values, which is the case for some investment grade government bonds in Europe in recent years. In this setting we focus on Amer- ican equity call and put options and characterize analytically their two-dimensional free boundary, i.e. the underlying equity and the interest rate values that trigger the optimal exercise of the option before maturity. We show that non-standard double continuation regions may appear, extending the findings documented in the litera- ture in a constant interest rate framework. Moreover, we contribute by developing a bivariate discretization of the equity price and interest rate processes that converges in distribution as the time step shrinks. This discretization, described by a recombin- ing quadrinomial tree, allows us to compute American equity options’ prices and to analyze their free boundaries with respect to time and current interest rate. Finally, we document the existence of non-standard optimal exercise policies for American call options on a non-dividend-paying equity

Coexistence states for periodic planar Kolmogorov systems

We prove the existence of positive periodic solutions for a class of predator prey periodic systems

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Esempi di problemi pratici risolvibili con la matematica finanziaria

Teoria dell'arbitraggio in tempo discreto e continuo : materiale didattico per il corso di Finanza quantitativa e derivati

Dispense per il corso di laurea specialistica Finanza Quantitativa e Derivati, I parte, Università Boccon

Non-myopic portfolio choice with unpredictable returns: the jump-to-default case

If a risky asset is subject to a jump-to-default event, the investment horizon affects the optimal portfolio rule, even if the asset returns are unpredictable. The optimal rule solves a non-linear differential equation that, by not depending on the investor's pre-default value function, allows for its direct computation. Importantly for financial planners offering portfolio advice for the long term, tiny amounts of constant jump-to-default risk induce marked time variation in the optimal portfolios of long-run conservative investors. Our results are robust to the introduction of multiple non-defaultable risky assets

American options and stochastic interest rates

We study fnite-maturity American equity options in a stochastic mean-reverting diffusive interest rate framework. We allow for a non-zero correlation between the innovations driving the equity price and the interest rate. Importantly, we also allow for the interest rate to assume negative values, which is the case for some investment grade government bonds in Europe in recent years. In this setting we focus on American equity call and put options and characterize analytically their two-dimensional free boundary, i.e. the underlying equity and the interest rate values that trigger the optimal exercise of the option before maturity. We show that non-standard double continuation regions may appear, extending the fndings documented in the literature in a constant interest rate framework. Moreover, we contribute by developing a bivariate discretization of the equity price and interest rate processes that converges in distribution as the time step shrinks. This discretization, described by a recombining quadrinomial tree, allows us to compute American equity options’ prices and to analyze their free boundaries with respect to time and current interest rate. Finally, we document the existence of non-standard optimal exercise policies for American call options on a non-dividend-paying equity

Dividend and Uncertainty: Evidence from the italian market

In this paper we investigate the behaviour of the market around dividend payment dates. Our empirical analysis, based on a Bayesian approach applied to Italian stock data, confirms the presence of abnormal returns at the ex-dividend date, as already documented in the literature for other markets. Calibrating a suitable model introduced in Battauz, Quadratic Hedging for Asset Derivatives with Discrete Stochastic Dividends, Insurance: Mathematics and Economics 32/2 (2003) to take care of the additional randomness pertubing the market around dividend payment dates, we investigate the effects on the derivative evaluation. Looking at the NoArbitrage prices of American call options written on some Italian dividend-paying stock and comparing them with the marketed prices, we conclude that the effect of this additional randomness can be neglected