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IAI Actuarial Core Principles · Economic Modelling · Valuing benefit guarantees using simulation

An insurer sold a single-premium policy with a 5-year guarantee of Rs 100 per Rs 100 invested in an equity fund. The guarantee is valued as a Black-Scholes put. All else equal, which change would increase the put value?

A rise in fund volatility increases the value of the guarantee put. Higher volatility raises the chance of a large shortfall below the guaranteed sum, while gains beyond the strike add nothing to the put. Higher rates, a higher fund value or a lower strike all reduce it.

  1. AA rise in the fund volatilityCorrect
  2. BA rise in the risk-free interest rate
  3. CA rise in the initial fund value S
  4. DA fall in the guaranteed sum
  5. A fall in the time to maturity, with volatility above zero

Explanation

A put's value rises with volatility since downside risk is larger while the upside is not penalised. A higher rate lowers the put through lower PV of strike, a higher S lowers it, a lower strike lowers it, and shorter maturity generally lowers it.

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