PT  - JOURNAL ARTICLE
AU  - Yaacov Z. Bergman
AU  - Alberto Bueno-Guerrero
TI  - General Restrictions on Prices of Financial Derivatives Written on Underlying Diffusions
AID  - 10.3905/jod.2022.1.168
DP  - 2022 Aug 31
TA  - The Journal of Derivatives
PG  - 119--143
VI  - 30
IP  - 1
4099  - https://pm-research.com/content/30/1/119.short
4100  - https://pm-research.com/content/30/1/119.full
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.