Computational recovery of time-dependent volatility from integral observations in option pricing

New Approximations to Bond Prices in the Cox–Ingersoll–Ross Convergence Model with Dynamic Correlation

“…A simple approximate solution of the bond pricing equation is useful in many applications, where an evaluation of the bond prices is necessary. We plan to focus our future work on using these approximations in inverse problems, similar to those in [24][25][26]. In particular, we are interested in estimating the implied correlation from the market data.…”

“…Since the terms multiplying the expressions above in (25) are O(1), being either independent of τ or an O(1) function ρ(T − τ), their products cannot be matched with O(τ ω−1 ) term on the left hand side. Therefore, the term being matched is h(r d , r u , τ), and if this function is O(τ µ ), then ω = µ + 1.…”