Exotic Derivatives Trading

February 19, 2009

Importance of Equity Interest rate correlation in Long term Autocallables

Filed under: Risk Management of Exotic Derivatives — Exotics Trader @ 3:23 pm

Consider a 7 yr Autocallable with 100% Auto call Barrier starting today.
End of 1st year: If Performance > 100%, EARLY REDEMPTION & client gets 100%
End of 7th year: If Performance > 100%, EARLY REDEMPTION & client gets 100%
P1 = Probability of it Auto calling in year 1 which depends on Spot & Volatility
P2 = Probability of it Auto calling in year 7 which again depends on Spot & Volatility

1-P2-P3 = Probability of it Not Auto calling & paying zero
So we hedge this structure using a portfolio of zero coupon bonds. In this case two bonds with maturity 1 yr & 7yr, the weightings of these bonds depend on the probability of structure autocalling.
e.g. when P1 = 50%, P2 = 30%, we buy 1yr bond worth 50% of the Notional & 7yr Bond worth 30% of the Notional to hedge our Autocallable, assuming we are short the structure.
Importance of equity interest rate correlation:
CASE 1: Assume the equity moves up!
If equity increases the probability of auto calling in the first year increases i.e. P1, Hence we need to buy 1yr bonds & sell the 7yr ones.
Sub-case 1: Correlation between interest rate & Equity is positive: So increasing equity would also increase Interest rate. However value of zero coupon 7yr bond (which we have to sell) would decrease more than the value of the zero-coupon 1yr bond (that we have to buy). (Because Duration of a 7yr bond > Duration of a 1yr bond). Hence we would make a net loss on the rebalancing of the Bond weightings.

Sub-case 2: Correlation between interest rate & Equity is negative: So increasing equity would decrease Interest rates. The value of a zero coupon 7yr bond (which we have to sell) would increase more than the value of the zero-coupon 1yr bond (that we have to buy). (Because Duration of a 7yr bond > Duration of a 1yr bond). Hence we would make a net profit on the rebalancing of the Bond weightings.

CASE 2: Assume the equity moves down!
If equity decreases the probability of auto calling in the first year decreases i.e. P1, Hence we need to sell 1yr bonds & buy the 7yr ones.
Sub-case 1: Correlation between interest rate & Equity is positive: So decreasing equity would also decrease Interest rate. However value of zero coupon 7yr bond (which we have to buy) would increase more than the value of the zero-coupon 1yr bond (that we have to sell). (Because Duration of a 7yr bond > Duration of a 1yr bond). Hence we would make a net loss on the rebalancing of the Bond weightings.

Sub-case 2:
Correlation between interest rate & Equity is negative: So decreasing equity would increase Interest rates. The value of a zero coupon 7yr bond (which we have to buy) would decrease more than the value of the zero-coupon 1yr bond (that we have to sell). (Because Duration of a 7yr bond > Duration of a 1yr bond). Hence we would make a net profit on the rebalancing of the Bond weightings.

In general equity – Interest rate correlation is governed by Inflation, Monetary policies & Macro-economic factors

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1 Comment »

  1. Hi,

    I like the above artical very much and would like to ask a question.

    I am currently analyzing the structured product called ‘Autocallable equity index linked notes’. I totally understand the term sheet and the position and payoff conditions for the investors, however, I wanna know what is actually behind this product in the issuer side. What are the derivatives that issuers have used to construct the notes and hedge against the market risks embedded in the basket of equity indices linked to the notes? How do they perform the financial engineering in this case?

    Here is the extracted term sheet of the notes:

    Linked index: Equity indices (Nikkei, DJ, and FTSE)
    Maturity: 4 years (10 May 2012)
    Reference level: Closing index value of Nikkei, DJ and FTSE on 5 May 2008
    Observation date: 5 May 2009, 5 May 2010, 5 May 2011
    Final reference date: 5 May 2012

    if on any observation date all the 3 indices have value > than the reference levels, then the note will be autocalled-back
    – if called back in 2009: investors can get 100% principle and 23% on top of its principle as additional earning
    – if called back in 2010: investors can get 100% principle and 40% on top of its principle as additional earning
    – if called back in 2011: investors can get 100% principle and 60% on top of its principle as additional earning

    if hold until maturity, then
    (i) If all the 3 index values above their reference levels
    – investors can get 100% principle and 94% on top

    (ii) if any 1 of the indices has value between 50% and 100% of its reference level
    – investors can get 100% principle

    (iii) if any 1 of the indices has value below 50% of its reference level
    – investors lose off and can only get back the % of principle reflecting the worst performing index

    With this term sheet, i know what is the risk and payoff for the investors, but can you please help me to figure out more about the issuer side? how they make this note? how they use options or bond etc. to construct the note and walk away from market risk to make profit?

    Thanks so much for your kind help!!!

    Comment by Gloria — January 15, 2010 @ 5:26 pm | Reply


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