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We develop a quantum algorithm to price discretely monitored lookback options in the Black-Scholes framework using imaginary time evolution. By rewriting the pricing PDE as a Schrodinger-type equation, the problem becomes the imaginary time evolution of a quantum state under a non-Hermitian Hamiltonian. This evolution is approximated with the Variational Quantum imaginary time evolution (VarQITE) method, which replac…
We propose a new, data-driven approach for efficient pricing of - fixed- and float-strike - discrete arithmetic Asian and Lookback options when the underlying process is driven by the Heston model dynamics. The method proposed in this article constitutes an extension of our previous work, where the problem of sampling from time-integrated stochastic bridges was addressed. The model relies on the Seven-League scheme, …
We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage probabilities. We combine efficient numerical quadrature with continuous-time Markov chain approximation for the first passage problem to price lookbacks. Our method is applicable to a variety of models, including one-di…
Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to infinity, thereby solving a problem posed by Lin and Palmer. We prove, in particular, that the price in the discrete model tends to the price in the continuous Black-Scholes model.…
In this article we study the convergence of a European lookback option with floating strike evaluated with the binomial model of Cox-Ross-Rubinstein to its evaluation with the Black-Scholes model. We do the same for its delta. We confirm that these convergences are of order 1/Sqrt(n). For this, we use the binomial model of Cheuk-Vorst which allows us to write the price of the option using a double sum. Based on an im…
Motivated by the pricing of lookback options in exponential Lévy models, we study the difference between the continuous and discrete supremum of Lévy processes. In particular, we extend the results of Broadie et al. (1999) to jump-diffusion models. We also derive bounds for general exponential Lévy models.
In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $θ(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their (zero-sum) game has the payoff kernel $W_θ(X)/D(X)$, where $W_θ(X)$ is the trader's final wealth and $D(X)$ is the final wealth that would have accrued to a $\$1$ deposit int…
Slow trend: lookbacks of roughly 6–12 months, low turnover, fewer whipsaws, later entries, and the bulk of classic CTA crisis convexity.
The workhorse speed: roughly 1–4 month lookbacks — enough signal to catch swings, enough noise to bleed in ranges.
Blend fast, medium, and slow trend signals in each market so the book is not a single lookback dressed as a diversified program.
Long currencies that appreciated over the lookback, short those that depreciated — cross-sectional FX momentum.
Long currencies that appreciated over the lookback, short those that depreciated — cross-sectional FX momentum.
Slow trend: lookbacks of roughly 6–12 months, low turnover, fewer whipsaws, later entries, and the bulk of classic CTA crisis convexity.
The workhorse speed: roughly 1–4 month lookbacks — enough signal to catch swings, enough noise to bleed in ranges.
Blend fast, medium, and slow trend signals in each market so the book is not a single lookback dressed as a diversified program.