Pricing derivatives using Monte Carlo Techniques Essay

Pricing derivatives using Monte Carlo Techniques - Essay Example In practice generic Monte Carlo pricing engines face computational problems in the presence of discontinuous payoffs options, because of above stated time consumption limitation but also due to poor convergence with its finite difference estimates and brute force perturbation. Benhamou (2001)[3] following Fourni et al. (1999)[4] use Malliavin calculus to smoothen the simulation function. Benhamou(2001)[3] assumes that the functions are smooth enough to be able to perform the different computation following technical assumptions enunciated earlier, in particular the assumption regarding uniform ellipticity of the volatility operator, in Benhamou (2000-i)[5] (2000-ii)[6] and Fourni et al. (2001)[7]. Benhamou (2001)[3] further states when using finite difference approximation for the Greeks, with jumped price and taking the sensitivity issues into account, errors on numerical computation of the expectation via the Monte Carlo, and another one on the approximation of the derivative funct ion occur. Analysis ends up approximating the second order derivative of the payoff function .An approximation is obviously very inefficient for very discontinuous payoffs like for binary, range accrual, barrier and other type of digital options. To reduce this inefficiency, Broadie and Glasserman (1996)[8] suggested using the likelihood ratio method. Benhamou says," All Greeks can be written as the expected value of the payoff times a weight function and thee weight functions are independent from the payoff function implying that for a general pricing engine, such as Monte Carlo, using certain (numerical) criteria of smoothness, one can branch on the appropriate method. Because it is in a sense independent from the payoff function, the general implementation is simpler that the one of variance reduction technique that only apply to very specific payoff (like the use of control variate).Also no extra computation is required for other payoff function as long as the payoff is a functi on of the same points of the Brownian trajectory. This can be cached in memory to make it efficient Benhamou (2001).Thus Mallavian calculus promises savings in terms of computations, complexity, cache memory and in time though it may produce some noise. The formidable amount of literature exists which intends to suggest analytical pricing formulae for single asset American options. It includes Carr(1998)[9], Grant et al(1997)[10], Bunch and Johnson(2000)[11],Huang et al(1996)[12], Geske and Johnson(1984)[13] and Barone Adesi and Whaley(1987)[14].One can even refer to older constructs like the binomial model of Cox et al(1979)[15].Many of these constructs deploy elaborate mathematical tools, like recursive integration schemes or

E-business Foundations and Basic Concepts Assignment

E-business Foundations and Basic Concepts - Assignment Example They are particularly responsible for specifying what needs to be purchased, the features that the product should have, the quantity to be bought and so on and so forth. In case of a more technically complex products, the buyer actually defines the product’s technical specifications. In the following stage the potential supplier who can supply the required product are sought out for. At this stage, the customer involved in the buying process (in this case a business) seeks out for information regarding the products that they require and the vendors who can meet their demand. Majority of the buyers begin their search online and thereafter attend industry trade shows and henceforth establishes contact with the suppliers either through email or telephone. In order to gain knowledge regarding a variety of supplier buyers also tends to discuss with industry experts, consult trade magazines as well as attend webinars conducted by vendors or perhaps pay a visit to their facilities. T he decision regarding the choice of qualified vendors rests in the hand of purchasing agents. The vendors who have been chosen are asked to complete responses relating to requests for proposal. The proposals are then evaluated and the suppliers are selected. Following this stage, an order routine is established and a post purchase evaluation is conducted and the feedback is reverted back to the vendor (Saylor, 2013). The buying process involved in business to consumer marketing is relatively simple and straightforward where the buyers just has to choose the required product and pay for it either through credit card, debit card or cash. The buyers have the flexibility to shop via online retailers which saves them the extra cost of transportation and as well as saves them the extra effort of being physically present in the shop. Instead they can shop online and pay via internet banking, debit and credit card (Ferrell,