Company XYZ has a convertible bond outstanding, that pays an annual coupon of 2.5% semi-annually, has a par value of $1,000, and that matures on February 15th, 2027. Company XYZ convertible bond has a conversion ratio of 25.

 

On March 7th, 2022, the stock price of Company XYZ is trading at $32, while the convertible bond in question has a quoted price of 99-28. The day count convention for this bond is 30/360. A Company XYZ straight bond (simple bond with no conversion, call or put features) of a similar maturity to this convertible bond is trading with a credit spread of 300 basis points. The yield on treasuries for all maturities is 1.50%. For purposes of options pricing, the risk-free rate is equal to 1.50% (simple interest).
The stock of Company XYZ pays a quarterly dividend of 16 cents. Lately and for the foreseeable future, Company XYZ maintains a constant dividend yield.

 

The monthly historical standard deviation of Company XYZ stock returns is equal to 9.75%.
A review of listed call options on Company XYZ shows the following implied volatility quotes (based on mid prices) for three maturities and six different strikes:

 

Strike	Jun 2022	Sep 2022	Jan 2023	Jan 2024
25	37.6%	36.0%	33.9%	30.6%
30	37.6%	35.3%	33.4%	30.1%
35	37.1%	34.9%	33.0%	29.7%
40	37.1%	34.3%	32.2%	28.9%
45	36.7%	33.7%	31.5%	28.1%
50	35.7%	32.8%	30.5%	27.1%

As a hedge fund manager, you are considering the Company XYZ convertible bond described above for a convertible bond arbitrage trade on March 7th, 2022.

 

Calculate the value and strike of the conversion option embedded in the Company XYZ convertible bond. Show your workings.

Answer rating: 100% (QA)

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