"The financial engineering process within investment banking"

speaker: Simone Freschi, Head of Trading MpsCapitalServices

The topics of this short lecture will be the:

an analysis of the structure of an investment bank

the mathematics suitable for the problems in the real world

trader point of view how has been the crisis and how the market is now different from before.

The structure of the Investment Bank

Capital Market Division

Marketing Division

Trading Division

Risk Control Unit

The mathematics of Variable Annuities

Variable annuities are also referred to as accumulator products or as GMxBs where, in the latter, the ‘x’

describes the nature of the guarantee in the prod uct, commonly known as the rider. Atypical ‘Guaranteed Minimum x Benefit’ might refer to Accumulation (GMAB), Income (GMIB),

Death (GMDB) or Withdrawal (GMWB).

The mathematics of Variable Annuities

I would like to analyse with you a product which is sold by the bank/insurance joint venture AXA/MPS. The unit linked is called Accumulator.Accumulator Investimento is a GMDB. The unit guarantee to the client a minimum capital at expiry given by the invested amount capitalized at a fixed contractual rate. The premium of the guarantee (which is a put in the hand of the client) is paid during the life of the contract as periodic fees. The client as also the faculty to redeem early and the insurance will pay the value equal to the NAV of the underlying funds less a penalty.

The mathematics of Variable Annuities

The product then guarantee at each date the maximum between:

a long position on the fund, plusa long position on a put that guarantee the minimum capital plusa short position on the fees to be paid plusa long position on the unwinding option AND

the Nav of the underlying funds less the penalty this means that the first term corresponds to the scomposition of the unit in the case the client has not redeem (and reserve the right to do at a later stage), the second term is what the client is obtaining early terminating at that date. Using the mathematica formula: 

Or

The mathematics of Variable Annuities