Path integral approach to the pricing of timer options with the Duru-Kleinert time transformation.

In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both the perpetual timer call options and the finite time-horizon timer call options. These general results allow us to find closed-form pricing formulas for both the perpetual and the finite time-horizon timer options under the 3/2 stochastic volatility model as well as under the Heston stochastic volatility model. For the treatment of timer options under the 3/2 model we will rely on the path integral for the Morse potential, with the Heston model we will rely on the Kratzer potential.

Path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models.

We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.

Postpartum hyperprolactinemia and hyporesponsiveness of growth hormone (GH) to GH-releasing peptide.

Human PRL and GH as well as their respective receptors have closely related origins. In peripartal women, physiological hyperprolactinemia is associated with a pronounced hyposomatotropism that remains to be fully characterized. Through paracrine mechanisms, PRL-secreting "pregnancy cells" may modulate the secretory function of somatotropes, which are known to express PRL receptors. Within a randomized, placebo-controlled design, we examined GH responsiveness in 10 nonpregnant women and in 58 mothers either in early (median, 48 h; range, 42-54 h after delivery; all lactating) or late postpartum (median, 10 weeks; range, 3-25 weeks; lactating and nonlactating subgroups), using GH-releasing peptide-1 (GHRP-1; 100-micrograms i.v. bolus) as the GH secretagogue. Baseline serum PRL concentrations were low and similar (median, 5 micrograms/L) in nonpregnant controls and nonlactating, late postpartum women and were elevated in lactating women, particularly in the early postpartum period (median, 102 micrograms/L), compared to those in the late postpartum period (median, 27 micrograms/L). GHRP-1 elicited GH responses in all study groups; lactation was associated with lower and slower GH responses. Serum GH concentrations (20 min after GHRP-1 treatment) in controls (median, 78 micrograms/L) were 7- and 5-fold higher than those in lactating women studied, respectively, early or late postpartum. Baseline prolactinemia presented an inverse correlation with GH responsiveness; the higher baseline PRL concentration, the lower and the slower the GH response to GHRP-1. GH hyporesponsiveness in postpartum women is herewith further characterized to include the GHRP pathway. The inverse relationship between baseline prolactinemia and GH responsiveness is consistent with the concept that pregnancy cells may exert, either directly or indirectly, an inhibitory effect on the secretory capacity of somatotropes.