sol10 - Solutions for Unit 10 Questions 1. A firms asset...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solutions for Unit 10 Questions 1. A firms asset value is modeled using Mertons model. Assume V = 1 , 000 , 000, and that the return rate on the assets is V = 0 . 1 The firm has issued a 3-year zero coupon bond with a face value of B = 500 , 000. (a) Find the volatility V of the firms return on its asset value if its probability of default is 0.06. Solution: We need to write the probability of default under Mertons model and solve for V : . 06 = P ( V T < B ) = P ( N (0 , 1) < (ln B- ln( V )- ( V- 2 V / 2) T ) / ( V T )) because under Mertons model, we have that ln V T N (ln V + ( V- 2 V / 2) T, 2 V T ), where here V = 10 6 , V = 0 . 1, B = 500 , 000, T = 3. Hence we need to have z . 06 = (ln B- ln( V )- ( V- 2 V / 2) T ) / ( V T ) , where z . 06 1 . 5551. Solving for V we find V = 0 . 31386. (b) Determine the expected fraction of money recovered by the lender when the firm defaults (given that there has been default). Use the fact that if X N ( a,b ) then E( e X 1 e X <c ) = exp( a + b/ 2) ((ln( c )- a- b ) / b ) , where, as usual, ( x ) = P ( N (0 , 1) x ). Solution: We need to compute E V T B | V T < B where ln V T N ( a,b ) with a = ln V + ( V- 2 V / 2) T and b = 2 V T . Hence the above expectation is equal to E V T B 1 V T <B /P ( V T < B ) = (1 /B )(exp( a + b/ 2) ((ln( c )- a- b ) / b )) / . 06 = 0 . 80635 , where c = B . Note that we take the expectation under the physical measure here, because we are not pricing....
View Full Document

This note was uploaded on 12/12/2010 for the course ACTSC 445 taught by Professor Christianelemieux during the Fall '09 term at Waterloo.

Page1 / 5

sol10 - Solutions for Unit 10 Questions 1. A firms asset...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online