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IAI Actuarial Core Principles · Economic Modelling · Principles of option pricing

A European put and a European call on the same non-dividend share have the same strike and expiry. Which statement about the effect of a rise in the risk-free interest rate, other factors unchanged, is correct?

A higher risk-free rate raises the call and lowers the put. It reduces the present value of the strike price, which benefits the buyer who pays the strike (call) and hurts the seller who receives it (put), as put-call parity shows.

  1. ABoth the call and the put increase in value
  2. BBoth the call and the put decrease in value
  3. CThe call increases in value and the put decreases in valueCorrect
  4. DThe call decreases in value and the put increases in value
  5. Neither is affected, because the rate only matters for American options

Explanation

A higher rate lowers the present value of the strike. The call holder pays the strike later, so the call gains. The put holder receives the strike later, so the put loses. Put-call parity, C - P = S - K e^(-rT), confirms this.

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