Inferring Interest Rates from Put–Call Parity and Checking Futures Consistency

Summary

The document derives an implied risk-free rate from European put–call parity. Starting from the relation between a call, a put, spot, and the discounted strike, it rearranges the equation to solve for the annualized rate using the option prices, strike, spot price, and time to expiry. The author applies this calculation to a set of market observations and reports an unexpectedly negative implied rate, despite describing the options as liquid.

The author also checks the call–put price difference against a quoted futures price, raising a question about consistency among the observed prices and parity relationships. However, the document contains no answer or resolution, so it does not establish the cause of the discrepancy. In practice, interpreting such an implied rate depends on matching contract and underlying conventions, expiry and day-count assumptions, and comparable tradable prices; the supplied question alone does not assess those factors or verify that the inputs satisfy the model’s assumptions.

Key ideas

• Put–call parity can be rearranged to infer a rate from option and spot prices.
• The calculation requires the strike, time to expiry, and matching call and put prices.
• The author reports a negative implied rate from the quoted observations.
• A futures-price check is raised as a consistency question, but no resolution is provided.
• Contract conventions and input comparability affect how an implied rate should be interpreted.

Tags

# calculating risk free interest rate from put call parity


# calculating risk free interest rate from put call parity












I'm trying to calculate the interest rate $r$ from the put-call parity. As per hull, put-call parity is given by the below equation.

$c + Ke^{-rT} = p + S_{0}$

where: $c$ = current call option price with stike=$K$ $p$ = current put option price with stike=$K$ $K$ = stirke price $S_{0}$ = spot price $r$ = annualized risk free interest rate $T$ = time till expiry in years

To calculate $r$ we can re-write the equation as\

$r$ = $-\frac {ln( \frac {p + S_{0} - c}{K})} {T}$

I'm trying to validate this against market data. I've below values from real market data $K$ = 10000 $c$ = 428.4 $p$ = 466.5 $S_{0}$ = 10107.6 $T$ = 13 days = (13/365) $F_{0}$ = 9961.5 (current future price)

when I plug these values into the equation I'm getting an interest rate of $-40.61\text{%}$. Am I missing something? These options contracts were liquid with a good bid-ask spread.

I also verify that $c - p + k = F_{0} $

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.