Abstract
The aims of this paper are twofold. Firstly, we present an approximating formula for pricing basket and multi-asset spread options, which genuinely extends Caldana and Fusai’s (2013) two-asset spread options formula. Secondly, under the lognormal setting, we show that our formula becomes a Black and Scholes type formula, extending Bjerksund and Stensland’s (2011). Numerical experiments and comparison with Monte Carlo simulations and other methods available in the literature are discussed. The main contribution of this paper is to provide practitioners with a pricing formula, which can be used for pricing basket and multi-asset spread options, even under a non-Gaussian framework.
Highlights
Multi-asset spread options are options whose payoff at maturity is given by the difference between two baskets of aggregated asset prices
Under the lognormal setting, we show that our formula becomes a Black and Scholes type formula, extending Bjerksund and Stensland’s (2011)
The main contribution of this paper is to provide practitioners with a general closed form approximation pricing formula, which can be used for real-time pricing of multi-asset spread options, even under a non-Gaussian framework
Summary
Multi-asset spread options (or basket-spread options) are options whose payoff at maturity is given by the difference (or so-called the spread) between two baskets of aggregated asset prices. The rest of the paper is outlined as follows: in Section 2 we present the general closed form approximation pricing formula for multi-asset spread options This is done via a procedure, which requires only a univariate Fourier inversion and it is applicable to models for which the joint characteristic function of the underlying assets is known in closed form. The second approximation formula discussed in [26] exploits the so-called arithmetic-geometric average inequality and consists in a generalization of the Vorst (1992)’s approach, see [16], to a characteristic function framework It does not require any optimization step in contrast with the above lower bound. Numerical experiments reported in [26], Section 5, show that the approximating formula based on the arithmetic-geometric average inequality is in general less accurate than the lower bound above
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