Based on Merton model of credit risk, I understand that investing in a risky debt is the same as buying a treasury bond and writing a put option on the firm's assets with a strike price equal to the face value of the debt. And the the equity is a call option on the assets of the borrowing firm with a strike price equal to the face value of the debt as shown in the diagrams below.
What i dont understand is why there is a negative relationship between the risk free interest rate and credit spread, which Merton has empirically shown. Intuitively, i would have thought the increasing the risk free interest rate would lower the discounted expected future cash flows and thus lead to higher probability of default and wider credit spreads. I found the possible explanations from some research papers:
"When interest rates rise, the value of the put option granted to the shareholders decreases because of the lowering of the discounted expected future cash flows, which in turn increases the value of the corporate bond since the creditors have a written put option position. This mechanism thus reduces the yield of the bond, making the spread over the yield of an equivalent risk-free security narrower. Another way of interpreting the outcome is to view the risk-neutral growth path of the firm value as being higher following an interest rate increase, leading to a lower probability of default and/or a lower default protection put option value, either way increasing the value of the corporate bond and therefore tightening the credit spread between corporate and risk-free government obligations."
"First, Merton (1974) argues that when the risk free rate increases, the present value of the future expected cash flow discount will de- crease, thus reducing the price of the put option. The investor of the corporate bond shorts put option, and the value of his long corporate bond position will increase. The increase of the price of the corporate bond will decrease the spread."
Can someone breakdown the Merton model and provide an intuitive explanation of why there may be a negative relationship between the risk free rate and credit spread?