RT Journal Article
SR Electronic
T1 General Restrictions on Prices of Financial Derivatives Written on Underlying Diffusions
JF The Journal of Derivatives
FD Institutional Investor Journals
SP jod.2022.1.168
DO 10.3905/jod.2022.1.168
A1 Yaacov Z. Bergman
A1 Alberto Bueno-Guerrero
YR 2022
UL https://pm-research.com/content/early/2022/08/22/jod.2022.1.168.abstract
AB We apply probabilistic solutions of parabolic PDEs with terminal and boundary conditions to obtain restrictions on contingent claims written on one-dimensional diffusions. For term structure derivatives, we obtain monotonicity and convexity results with respect to the short-term interest rate. We apply them to bonds, calls on bonds and puts on interest rates and we find a condition for the price of these derivatives to be convex in that rate. We find that yield curves corresponding to higher short-term rates lie uniformly above curves with lower rates. Regarding options on assets with local volatility, we obtain probabilistic representations, bounds and asymptotic results for delta, rho, and theta. Similar results are obtained for Asian options.