Question

Derivatives and risk management: OPTIONS PRICING

-What is meant by put-call parity?

-How does the concept of a synthetic call (i.e. long call and a long put) set the stage for put-call parity?

-How does this result in an equilibrium value for a put option?

Answer 1

Put-call parity is a principle that defines the relationship between the price of European put options and European call options of the same class, that is, with the same underlying asset, strike price and expiration date. Put-call parity states that simultaneously holding a short European put and long European call of the same class will deliver the same return as holding one forward contract on the same underlying asset, with the same expiration, and a forward price equal to the option's strike price. If the prices of the put and call options diverge so that this relationship does not hold, an arbitrage opportunity exists, meaning that sophisticated traders can theoretically earn a risk-free profit. Such opportunities are uncommon and short-lived in liquid markets.

The equation expressing put-call parity is:

C + PV(x) = P + S

where:

C = price of the European call option

PV(x) = the present value of the strike price (x), discounted from the value on the expiration date at the risk-free rate

P = price of the European put

S = spot price or the current market value of the underlying asset .

2 question:

A synthetic call, or synthetic long call, is an options strategy in which an investor, holding a long position in a stock, purchases an at-the-money put option on the same stock to protect against depreciation in the stock's price. It is similar to an insurance policy.

A synthetic call is also known as a married put or protective put. The synthetic call is a bullish strategy used when the investor is concerned about potential near-term uncertainties in the stock. By owning the stock with a protective put option, the investor still receives the benefits of stock ownership, such as receiving dividends and holding the right to vote, In contrast, just owning a call option, while equally as bullish as owning the stock, does not bestow the same benefits of stock ownership.

Synthetic Call

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What is a 'Synthetic Call'
A synthetic call, or synthetic long call, is an options strategy in which an investor, holding a long position in a stock, purchases an at-the-money put option on the same stock to protect against depreciation in the stock's price. It is similar to an insurance policy.

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BREAKING DOWN 'Synthetic Call'
A synthetic call is also known as a married put or protective put. The synthetic call is a bullish strategy used when the investor is concerned about potential near-term uncertainties in the stock. By owning the stock with a protective put option, the investor still receives the benefits of stock ownership, such as receiving dividends and holding the right to vote, In contrast, just owning a call option, while equally as bullish as owning the stock, does not bestow the same benefits of stock ownership.

A chart showing the safety provided by a synthetic call, or married put.

Both a synthetic call and a long call have the same unlimited profit potential since there is no ceiling on the price appreciation of the underlying stock. However, profit is always lower than it would be by just owning the stock. An investor's profit decreases by the cost or premium of the put option purchased. Therefore, one reaches breakeven for the strategy when the underlying stock rises by the amount of the options premium paid. Anything above that amount is profit.

The benefit is from a floor which is now under the stock. The floor limits any downside risk to the difference between the price of the underlying stock at the time of the purchase of the synthetic call and the strike price. Put another way, at the time of the purchase of the option, if the underlying stock traded precisely at the strike price, the loss for the strategy is capped at exactly the price paid for the options.

3 question :

A portfolio comprising a call option and an amount of cash equal to the present value of the option's strike price has the same expiration value as a portfolio comprising the corresponding put option and the underlier. For European options, early exercise is not possible. If the expiration values of the two portfolios are the same, their present values must also be the same. This equivalence is put-call parity. If the two portfolios are going to have the same value at expiration, they must have the same value today, otherwise an investor could make an arbitrage profit by purchasing the less expensive portfolio, selling the more expensive one and holding the long-short position to expiration.