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athos


Total Posts: 2
Joined: Jul 2014
 
Posted: 2017-03-20 14:02
On Page 24-25 of N. Taleb's "Dynamic Hedging" the author talks about "Soft American Options"

> A *soft American option* (also called a pseudo-European option) is only
> subjected to early exercise from the standpoint of the financing of
> the intrinsic value.
>
> An *extension* of this definition is that only one interest rate, that
> affecting the the financing of the premium for the operator, impacts
> the decision to early exercise.
>
> For risk management and trading purposes, soft American options will
> be largely similar to the European options, except when interest rates
> become very high relative to volatility. The reason they are often
> called pseudo-European options is that they behave in general like
> European options, except when very deep in the money. The test of
> early exercise is whether the total option value is less than the time
> value of the money between the time of consideration and expiration.
>
> Example: Assume that an asset trades at $100, with interest rates at
> 6% (annualized) and volatility at 15.7%. Assume also that the 3-month
> 80 call is worth $20, at least if it is American. Forgoing early
> exercise would create an opportunity cost of 20 x 90/360 x .06 = .30
> cents, the financing of $20 premium for 3 months. The time value of
> the equivalent put is close to zero (by put-call parity), so the
> intelligent operator can swap the call into the underlying asset and
> buy the put to replicate the same initial structure at a better cost.
> He would end up long the put and long the underlying asset.

I have three questions here

Q1. My understanding is, "soft american options" are in general call options, that the option's value is due to the increasing of the stock value. Since stock value grows faster than interest rate, it's not advisable to early execute, unless, the interest rate is too high. The other case is put options, as time goes by, stock price increases and options' intrinsic value decreases, it's more advisable to early execute. Is my understanding correct?

Q2. How did Taleb come to the conclusion that "Forgoing early exercise would create an opportunity cost of 20 x 90/360 x .06 = .30 cents, the financing of \$20 premium for 3 months. "? I couldn't figure out why the financing cost of an American options, is the difference between an American and an European option's price.

Q3. Taleb says "so the intelligent operator can swap the call into the underlying asset and buy the put to replicate the same initial structure at a better cost", I do agree that call = asset + put, i.e. a call option can be replicated by an asset and a put, but why such replication has a better cost?





C'est par la logique qu'on démontre, c'est par l'intuition qu'on invente.

TakeItAndRun


Total Posts: 88
Joined: Apr 2010
 
Posted: 2017-03-27 09:46
Think in terms of arbitrage opportunity for question 1 and 3. As for Q2 30 cents is just the cost of carry for the call.

For instance Q3:
1/ Buy the call, wait for three months and exercise it:
Cost = call price + cost of carry + exercise price = 20 + 0.3 + 80 = 100.3
2/ Buy the put and the asset, wait for three months:
Cost = put price + asset price + cost of carry = 0.01 + 100 + 0.00015 + 1.5 = 101.51015

After three months, the portfolio in case 1/ or 2/ consists of the same asset. Strategy 1 is cheaper than strategy 2 contrary to N. Taleb's conclusion.

I think John C. Hull's book is far better than Dynamic Hedging.
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