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In optional redemption at the option of the lender, must you still price according to the "worst case"

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asked Oct 17, 2016 in BUS 2016H - Financial Mathematics by Valentine (520 points)

On page 21 of the Chapter 12 notes on Vula, the example reads

"A fixed interest stock with a coupon of 8% per annum payable half-yearly in arrears can be redeemed at the option of the lender at any time between 10 and 15 years from the date of issue.

What price should an investor subject to tax at 25% on income and capital gains, who wishes to obtain a net yield of at least 7% per annum, pay for R100 nominal of this stock?" 

The solution says that there is gain on capital (I agree) and says that redemption is on the latest possible date (n=15), but why would an investor choose the worst case scenario if they can choose when to redeem to contract and thus choose the best case scenario?

1 Answer

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answered Oct 17, 2016 by clarewalker (300 points)
selected Oct 18, 2016 by Richard van Gysen
 
Best answer

Hi Valentine

The practice when finding a price given a minimum yield is to price assuming worst case regardless of whether the option is at the lender or the borrower. 

I guess this is because although they may theoretically never choose n = 15, in practice they may have to and if they had priced for n = 10, this would result in a yield lower than 7%.

commented Oct 17, 2016 by simon_rigby (4,220 points)

So I guess the key phrase is "wishes to obtain a net yield of at least 7% p.a."? So, in a sense, the price depends on the buyer's preferences and risk appetite, and another buyer may assume that the bond will be redeemed in the best-case scenario, resulting in a different price? You're welcome to correct me, I'm just trying to understand :)

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