The following information is available to you in relation to the pricing of a binary option with a maturity of 1 year: Underlying price, So: $40.67 Risk free rate, r: 5.3% p.a. N(d2): 0.5477 Using this information, please calculate the price of a Put - Binary (Cash or Nothing) that has the same strike as the current underlying price, and the same maturity. (Please round your answer to 2 decimal places)
Question
The following information is available to you in relation to the pricing of a binary option with a maturity of 1 year: Underlying price, So: $40.67 Risk free rate, r: 5.3% p.a. N(d2): 0.5477 Using this information, please calculate the price of a Put - Binary (Cash or Nothing) that has the same strike as the current underlying price, and the same maturity. (Please round your answer to 2 decimal places)
Solution
A binary put option (also known as a cash-or-nothing put option) pays a fixed amount of cash if the price of the underlying asset is below the strike price at expiration, and nothing otherwise.
The formula to calculate the price of a binary put option is:
Binary Put Price = e^(-rt) * (1 - N(d2))
where: e = the base of the natural logarithm (approximately 2.71828) r = risk-free interest rate t = time to maturity N(d2) = the cumulative standard normal distribution function evaluated at d2
Given the details in the question:
r = 5.3% = 0.053 (as a decimal) t = 1 year N(d2) = 0.5477
We can substitute these values into the formula:
Binary Put Price = e^(-0.053*1) * (1 - 0.5477) Binary Put Price = 0.9481 * 0.4523 Binary Put Price = 0.4289
Therefore, the price of the binary put option is approximately $0.43 (rounded to two decimal places).
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