Lets consider the following story. A manufacturing firm is supposed to receive $100 million from a
client in six months. The firm expects to invest the money in purchasing machinery in one year. Thus,
it needs to manage it over the period between 6 months
Convexity may have value
Is there a hedging strategy which ensures duration hedging and
arbitrage gain from convexity trading in the case that YTM curves display
parallel shift? To check it, we form an arbitrage portfolio and neutralize
Analysis of Example 3.10 in
V0 $1,000,000, T 30
Face value of the T-bond: $1,000,000
Annuity pays $28,768 in six months for 30 years.
Let DC t0 , DA t0 , and DD t0 denote the duration of
the 30-year T-bond, 30-year annuity,
6.1.2 Margins and Mark-to-Market
6.1.3 The Convergence Property of Futures Prices
6.1.4 Futures versus Forwards
6.1.5 Hedging with Futures or Forwards?
4.1.1 The Convexity of Zero Coupon Bonds
4.1.2 The Convexity of a Portfolio of Securities
4.1.3 The Convexity of a Coupon Bond
4.1.4 Positive Convexity: Good News for Average
2.1.1 Discount Factors across Maturities
2.1.2 Discount Factors over Time
The discount factor between two dates, t and T, provides the term
of exchange between a given amount
Basics for Bond Markets
Do not distribute outside the class.
This is the intellectual property of Pro. Won.
Ajou University, Suwon, Korea
What is interest rate?
What is the discount factor?
Which risks are involved in holding
Long or Short hedge?
The direction of hedging
Suppose an investor plans to purchase a bond at
time in the future. He worries about decline in
What is an hedging strategy? Long or short?
Here hedging means he is guaranteed to purchase
Put-Call Parity for European
max cfw_ AT , BT max cfw_ AT BT ,0 + BT
= max cfw_BT AT ,0 + AT
where max cfw_ AT BT ,0 is a call payoff with strike price BT
and max cfw_BT AT ,0 is a put payoff with strike pri
Note on Chapter 3: Duration
3.2.1 Duration of a Zero Coupon Bond
Duration of a security is the (negative of the) percent
sensitivity of its price to a small parallel shift in the
level of interest rates
For a Zero Coupon Bond we get: