### Syllabus E3a)

a) Evaluate, for a given hedging requirement, which of the following is the most appropriate given the nature of the underlying position and the risk exposure:

iv) Interest rate options.

### Interest rate options calculations are very similar to Interest rate futures calculation

**Call options = right to buy**

Here we deposit some money - so we want to hedge against a fall in interest rates

To do this we want the option to buy futures (a call option)

**Put options = right to sell**

Here we borrow money so we need to hedge against an increase in interest rates

To do this we want the option to sell the futures ( a put option)

#### Exam standard example (extract)

MooFace Co is expecting to receive $48,000,000 on 1 February 2014, which will be invested until it is required for a large project on 1 June 2014 (meaning it will have 4 months to deposit money)

MooFace can invest funds at the relevant inter-bank rate less 20 basis points.

The current inter-bank rate is 4.09%.

Assume that it is 1 November 2013 now.

Expected futures price is $94·55 (If interest rates increase by 0·9%)

Expected futures price is $96·35 (If interest rates decrease by 0·9%)

The return on the futures market is 4.58%.

Options on three-month $ futures, $2,000,000 contract size, option premiums are in annual %

callsdecember |
callsmarch |
callsjune |
strike |
putsdecember |
putsmarch |
putsjune |

0.342 | 0.432 | 0.523 | 94.50 | 0.090 | 0.119 | 0.271 |

0.097 | 0.121 | 0.289 | 95.00 | 0.312 | 0.417 | 0.520 |

**Required**

Recommend a hedging strategy for the $48,000,000 investment, if interest rates increase or decrease by 0.9%.

#### Solution

Assume that MooFace will deposit $48,000,000 and therefore need to hedge against a fall in interest rates and buy call options.

MooFace needs 32 March call option contracts ($48,000,000/$2,000,000 x 4 months/3 months).

Note:

Time period required for deposit = 4 months (1 February - 1 June).

Period of the call option = 3 months (it is always 3 months)

Contract size $2,000,000 (given in the question)

If interest rates increase by 0·9% to 4·99% (= 4.09% + 0.9%) | ||

Exercise price | 94.50 | 95.00 |

Futures price | 94.55 | 94.55 |

Exercise ? | Yes | No |

Gain in basis points | 5 | 0 |

Underlying investment return ( 4.99% - 20 basis point) = 4·79% x 4/12 x $48,000,000 | $766,400 | $766,400 |

Gain on options (0·0005 x 2,000,000 contract size x 3/12 x 32 contracts, 0) | $8,000 | $0 |

Premium | ||

0·00432 x $2,000,000 x 3/12 x 32 | $(69,120) | |

0·00121 x $2,000,000 x 3/12 x 32 | $(19,360) | |

Net return | $705,280 | $747,040 |

Effective interest rate ($705,280 ($747,040) / $48m x 12/4months) | 4·41% | 4·67% |

If interest rates increase by 0·9% to 3.19% (= 4.09% - 0.9%) | ||

Exercise price | 94.50 | 95.00 |

Futures price | 96.35 | 96.35 |

Exercise ? | Yes | Yes |

Gain in basis points | 185 | 135 |

Underlying investment return (3.19% - 20 basis point=) 2·99% x 4/12 x $48,000,000 = | $478,400 | $478,400 |

Gain on options | ||

(0·0185 x 2,000,000 x 3/12 x 32) | $296,000 | |

(0·0135 x 2,000,000 x 3/12 x 32) | $216,000 | |

Premium | ||

As above | $(69,120) | |

As above | $(19,360) | |

Net return | $705,280 | $675,040 |

Effective interest rate ($705,280 ($675,040) / $48m x 12/4months) | 4·41% | 4.22% |

#### Discussion

The March call option at the exercise price of 94.50 seems to fix the rate of return at 4.41%, which is lower than the return on the futures market and should therefore be rejected.

The March call option at the exercise price of 95.00 gives a higher return compared to the FRA and the futures if interest rates increase, but does not perform as well if the interest rates fall.

If MooFace takes the view that it is more important to be protected against a likely fall in interest rates, then that option should also be rejected.