The multinomial option pricing model and its Brownian and Poisson limits

The Cox, Ross, and Rubinstein binomial model is generalizedto the multinomial case. Limits are investigated and shown toyield the Black-Scholes formula in the case of continuous samplepaths for a wide variety of complete market structures. In thediscontinuous case of Merton-type formula is shown to result,provided jump probabilities are replaced by their correspondingArrow-Debreu prices.     

Simple binomial processes as diffusion approximations in financial models

A binomial approximation to a diffusion is defined as 'computationallysimple' if the number of nodes grows at most linearly in thenumber of time intervals. It is shown how to construct computationallysimple binomial processes that converge weakly to commonly employeddiffusions in financial models. The convergence of the sequenceof bond and European option prices from these processes to thecorresponding values in the diffusion limit is also demonstrated.Numerical examples from the constant elasticity of variancestock price and the Cox, Ingersoll, and Ross (1985) discountbond price are provided.     

The upstairs market for large-block transactions: analysis and measurement of price effects

This article develops a model of the upstairs market where ordersize, beliefs and prices are determined endogenously. We testthe model's predictions using unique data for 5,625 equity tradesduring the period 1985 to 1992 that are known to be upstairstransactions and are identified as either buyer or seller initiated.We find that price movements prior to the trade date are significantlypositively related to trade size, consistent with informationleakage as the block is 'shopped' upstairs. Further, the temporaryprice impact or liquidity effect is a concave function of ordersize, which may result from upstairs intermediation.     

Signaling with dividends and share repurchases: a choice between deterministic and stochastic cash disbursements

We study firms signaling with cash disbursements and show thatthe choice of a deterministic or a stochastic disbursement dependson a property of the firm's production function that is analogousto absolute risk aversion for a utility function. With decreasing(increasing) absolute risk aversion, the high-quality firm prefersto distinguish itself from the low-quality firm with a stochastic(deterministic) outlay. We then study in detail two common formsof corporate cash distributions: dividends, a deterministicdisbursement, and share repurchases, a stochastic disbursement.     

Affordable retirement: light at the end of the tunnel

Compared to previous studies, the 2004 Replacement Ratio Study from Aon Consulting/Georgia State University shows an increase in the amount of income today's workers need at retirement to maintain their preretirement standard of living. After describing the study's replacement ratio findings, the authors estimate lump sums needed at retirement and required adjustments for both nonincreasing annuities and retiree medical expenses. They then describe steps innovative plan sponsors can take to encourage participants to understand and undertake their responsibility to acquire the substantial personal savings needed for a comfortable retirement.     

Sounds great, but what's in it for me? Helping employees understand their role in the retirement planning process

The communication of retirement plans by employers to their workers has greatly improved, but in many cases still falls short of getting employees to understand their roles in planning for their own retirement. The author states that a well-designed personalized retirement savings education program encourages employees to take ownership of their retirement plan. Three employee profiles are examined in the context of the personalized retirement education process.