**Triangular class exercise****$-based spot market quotes in LSE**Spot Rate 1: $ 1 = ¥ 107.91

Spot Rate 2: $ 1 = € 0.87

**1.) Calculate the implied rate!**The implied rate is calculated by (e.g.) dividing Spot Rate 1 by Spot Rate 2.

1 $ / 1 $ = ¥ 107.91 / € 0.87 <=>

<=> 1 = ¥ 107.91 / € 0.87 <=> | * 0.87 €

<=> € 0.87 = ¥ 107.91 <=> | / 0.87

<=> € 1 = ¥ 107.91/0.87 <=>

<=>

**Implied rate: € 1 = ¥ 124,03** (rounded)

**Tokyo Spot Market**

Quoted rate€ 1 = ¥ 128,03

**2.) Execute a full arbitrage!**Assumption 1: We own 1,000,000 Euro.

**Step 1: Find out, where Euro € is expensive.**London: € 1 = ¥ 124,03 (rounded implied rate, cf. first task)

Tokyo: € 1 = ¥ 128,03

So the Euro is more expensive in Tokyo. Therefore we sell our Euros in Tokyo, "go" to

the LSE (London Stock Exchange), buy Dollars $ with our Yen ¥ there and finally buy

Euros with the obtained dollars. At the end we should have an amount of Euros that

exceeds the amount at the beginning.

Step by step:

**Step 2: Buy Yen ¥ at TSE (Tokyo Stock Exchange)**Spot rate: € 1 = ¥ 128,03

Therefore: € 1,000,000 = ¥ 128,030,000

We just bought ¥ 128,030,000.

**Step 3: "Go" to London and buy Dollars**Spot rate: $ 1 = ¥ 107.91

Therefore: x = ¥ 128,030,000 / 107.91 ¥/$ = $ 1,186,451.67

We now have $ 1,186,451.67 and want to convert them back to Euros.

Step 4: Buy Euros with the newly obtained DollarsSpot rate: $ 1 = 0.87 €

==> 1 € = 1 $ / 0.87 = 1.15 $ (rounded)

Therefore: x = $ 1,186,451.67 / 1.15 $/€ = € 1,032,212.96 (exact exchange rate used)

We finally have

**€ 1,032,212.96**.

Comparison before-after:

**Before** | **After** |

€ 1,000,000 | € 1,032,212.96 |

Difference: + € 32,212.96 |

**3.) Look up the exchange rates for****o $ vs. ¥**: $ 1 = 97,8700 ¥ 23.04. 18:57:10

**o $ vs € **: $ 1 = 0,7649 € 23.04. 18:55:04

**o Calculate the implied rate!**(for calculation see task 1)

Implied rate: € 1 = 127,95 ¥

END (Hopefully I didn't miss any task).

Sincerely yours,

Javier Friedlmeier