SOA QFI QFQuantitative Finance & Investment — Quantitative Finance

If $dS=\mu S\,dt+\sigma S\,dW$, then $d(\ln S)$ equals:

Which model guarantees non-negative rates when Feller's condition holds and has an analytic bond price?

A 5-year CDS on a name with flat hazard rate 2% and recovery 40% has an approximate fair spread of:

Antithetic variates reduce Monte Carlo variance most when the payoff is:

Derive the Black–Scholes partial differential equation for a European derivative $V(S,t)$ on a non-dividend stock, stating assumptions. Then explain why the real-world drift $\mu$ does not appear.

An insurer wants a short-rate model to value interest-rate guarantees in annuities. Compare Vasicek, CIR and Hull–White on (i) mean reversion, (ii) possibility of negative rates, (iii) fit to the initial term structure, (iv) tractability, and recommend one with justification.

Explain the Merton structural model of default and compute the distance to default for a firm with asset value 120, debt face 100 due in one year, asset drift 6% and asset volatility 25%. Discuss two limitations of the model.

Explain the concept of asset-liability management (ALM) duration matching for a life insurer, and describe one limitation of simple duration matching that convexity matching addresses.