On March 2, a Treasury bill expiring on April 20 had a bid discount of 5.86, and an ask discount of 5.80. Calculate the best estimate of the risk-free rate to be used in valuing options with the Black Scholes Merton model.

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I did it with binomial model as follows:

There are 49 days from 2 March to 20 April

I found discount from the portfolio

Discount = 5.83 * (49/360) = 0.794

And then i found the price = face value - discount =100-0.794=99.2065

Finally I found the yield = $$(100/99.2065)^{(365/49)} - 1 =0.06113$$

This is solution with binomial model.

However, I cannot do its solution with black Scholes Merton model. Please help me in this point.

Thanks a lot

• You don't need the Tbill yield. Once you have the price of the Tbill you find the annualized continuous time interest rate by solving 100/99.2065=exp(r∗49/365) for r. Once you have r you can use it in the Black Scholes or Black Scholes Merton method, but first you have to find r. My solution is r=5.9343%, please check it. – noob2 Mar 15 at 10:51