# Physically Settled Options

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Contents

## What to Expect From Ledgerx’s ‘Physically-Settled’ Bitcoin Options

Institutional trading and clearing platform Ledgerx is preparing to offer ‘physically-settled’ bitcoin options. The company is currently waiting for full regulatory approval from the U.S. Commodity Futures Trading Commission (CFTC) to trade and clear bitcoin options. Bitcoin.com caught up with CEO Paul Chou to find out more about their upcoming bitcoin derivatives products.

Ledgerx has two registration applications pending with the CFTC. The first is as a swap execution facility (SEF), for which it received a temporary registration approval from the Commission in September 2020. The other is as a derivatives clearing organization (DCO), which any clearinghouse must register as before providing clearing services with respect to futures contracts, options on futures contracts and swaps.

“If approved, Ledgerx would be the first federally regulated bitcoin options exchange and clearinghouse to list and clear fully-collateralized, physically-settled bitcoin options for the institutional market”, the company’s website claims.

In December, Miami International Holdings (MIH) announced the completion of an investment in Ledgerx’s parent company, Ledger Holdings. Early investors of the company include Google Ventures and Lightspeed Venture Partners, a venture capital firm out of Menlo Park, California. The latest investment provides Ledgerx with “the capital that is critical to help us meet the minimum financial requirements necessary to be approved as a DCO and SEF by the CFTC”, Chou remarked at the time.

While pending CFTC’s approval, the company is “restricted from any live trading or clearing activities”, Chou told Bitcoin.com.

## What Products Will Be Offered?

Bitcoin.com (BC): What and how many products will Ledgerx offer?

Paul Chou (PC): Ledgerx will initially list vanilla puts and calls on bitcoin with standardized strikes and expirations. Strikes will be in a range around the current spot price and expirations will be from one-to-six months in tenor.

BC: Where will these products be listed?

PC: The products will be listed on the Ledgerx SEF (Swap Exchange Facility) and cleared by the LedgerX DCO (Derivatives Clearing Organization). We’re an integrated exchange and clearing operation so all parts of the transaction lifecycle from contract listing, trade matching, to final settlement are handled by us.

BC: Can you explain what “fully-collateralized, physically-settled bitcoin options” mean?

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PC: Ledgerx’s focus is on physically-settled options. This means that the long holder of the option has the right to purchase, in the case of a call, or sell, in the case of a put, actual bitcoin. This is in contrast to derivatives that are cash-settled, where the holder receives fiat.

Many of our customers transact in bitcoin in the course of their business, so physically-settled options that deliver bitcoin are more useful to them.

BC: What is the benefit?

PC: Accepting bitcoin as collateral at the clearinghouse enables us to fully-collateralize physically-settled positions such as short call options, ensuring that the clearinghouse holds the full deliverable for all trades.

This model reduces risk for participants and enables comfort around clearing a new, volatile asset class. A long option holder will never have to worry about taking a forced haircut on his expected bitcoin deliverable.

## Potential Customers

PC: Any participant who is an Eligible Contract Participant (as defined by the Commodities Exchange Act) may participate in trading on the Ledgerx SEF. Under this definition, retail would not qualify, but a range of hedgers and professional investors would be eligible.

BC: How much interest do you expect these products to garner?

PC:

We have significant demand from companies within the Bitcoin ecosystem, such as natural hedgers, as well as trading firms that are interested in the opportunity presented by a new options market.

BC: What is Ledgerx spending its time on while waiting for the CFTC’s approval?

PC: In addition to continuing various tests of the platform, we’ve been working on product development for other derivatives we can list down the line. We expect to have a range of interesting digital currency-related products that will suit both hedgers and investors / speculators; these products will look nothing like traditional financial derivatives and we aim to introduce them later this year.

What do you think of Ledgerx’s physically-settled derivatives products? Let us know in the comments section below.

Images courtesy of Shutterstock, Ledgerx, and CFTC

## American-Style Options

American-Style option contracts can be exercised at any time up to the option’s expiration. Most US listed stock options are American-style. Also, see European-Style Options.

The Ask Price, also called offer or simply ask, is a price a seller is willing to accept for stock, option, or any other trading instrument. Also, see Bid Price.

#### At-The-Money (ATM)

An option is At-The-Money when the strike price is the same as the underlying asset price. Also, see In-The-Money and Out-Of-The-Money.

Beta is a ratio measuring the movement of an underlying asset compared to the market as whole вЂ“ typically the S&P 500. If the beta equals 1, then the asset moves very closely to the market. If the beta is greater than 1, then the asset moves more aggressively than the market. If the beta is -1, then the asset moves exactly opposite of the market.

#### Bid Price

The Bid Price, or simply bid, is the highest price that a buyer is willing to pay for a stock, option or other trading instrument. Also, see Ask Price.

Buy To Close is closing a short position by buying the option back. Since an option can be bought to open or bought to close, BTC makes it clear the intent is to close the position. Also, see Buy To Open, Sell To Close, and Sell To Open.

Buy To Open is opening a long position by buying the option. Since an option can be bought to open or bought to close, BTO makes it clear the intent is to open a position. Also see Buy To Open, Sell To Close, and Sell To Open.

#### Call Option

A Call option, or simply call, is a contract that gives the owner the right to buy the underlying asset at the optionвЂ™s strike price. If the owner exercises the right to buy, a seller of the same call option has the obligation to provide the underlying asset to the owner.

#### Cash Settled

Cash settled options deliver the cash value of the underlying security when the option is exercised. Index options are typically cash settled. Also, see Physically Settled.

#### Delta

The amount that the option price will change for a one point change in the underlying asset.

## European-Style Options

European-Style option contracts can only be exercised near the option’s expiration, typically the last trading day before expiration. Also, see American-Style Options.

#### Expected Value

If the spread were traded a very large number of times, this is the amount that the trader can expect to win or lose on average for each trade of the spread. Positive values indicate that the spread has a profitable Expected Value. This column is available in the Search panel.

The Expected Value is evaluated over an underlying price range of +/-3 standard deviations. Throughout this range, the spread value at each underlying price is multiplied by the probability of the underlying moving to that price. Finally, all of the resulting products are added together to arrive at the Expected Value. The Expected Value may also be described as the Mathematical Expectation 1 .

1 The book The Mathematics of Options Trading by C.B. Reehl (ISBN 0-07-144528-5) was used as a reference for calculating the probability related columns. A specific trading example can be found on pages 123 вЂ“ 129.

#### Federal Funds Rate

In the United States, the federal funds rate is the interest rate at which banks charge each other for loans.

#### Gamma

Gamma measures the expected change in an option’s delta for a 1-point change in the price of the underlying asset. This is used to estimate the delta values as the asset price moves.

#### Historical Volatility

Historical Volatility (also called Hist Volatility) is a percentage calculated by the actual price changes of an underlying asset over a specific period of time. Sometimes this value is called Statistical Volatility.

#### In-The-Money (ITM)

In-The-Money is the term used, in the case of a call option, when the underlying asset price is higher than the strike price. For a put, an option is ITM when the underlying asset price is lower than the strike price of the option. Also, see At-The-Money and Out-Of-The-Money.

#### Intrinsic Value

Intrinsic Value refers to the ITM (In-the-Money) portion of the option premium, and is the difference between the underlying asset price and the strike price, i.e.:

Calls: AssetPrice вЂ“ StrikePrice = Intrinsic Value

Puts: StrikePrice вЂ“ AssetPrice = Intrinsic Value

If the calculation results in a negative number, the zero is used as Intrinsic Value.

The remaining premium that is not Intrinsic consists of Extrinsic Value.

#### Mid Price

The mid price is the average of the bid and ask prices, i.e.:

(Bid + Ask) / 2 = Mid Price.

#### Natural Price (also Natural)

The price that is typically used when sending a market order. When buying an option, the natural price would be the ask. When selling an option, the natural price would be the bid.

#### Option

An option is a derivative financial instrument based on the price of an underlying asset like a stock, index, or futures.

#### Option Symbology Initiative (OSI)

For over 3 decades, the symbols used to represent options were cryptic and difficult to determine what underlying asset they belonged to вЂ“ much less what option type was or when it expired. The Option Symbology Initiative (OSI) has changed that as of February of 2020.

Here is an example of how TradeStation displays an option symbol using the new OSI style.

Using this symbol, you can see the:

• Underlying Asset (AAPL)
• Expiration Date (110701 or July 1, 2020)
• Option Type (C for call or P for put)
• Strike Price (in this case 340 strike)

#### Pos Delta

The total Deltas of a position (single spread Delta * # of spreads in position * # shares per contract).

#### Option Term

An underlying asset can have options that last different amounts of time. This is the Term of the option. Option terms can include Weekly, Monthly, Quarterly, or EOM (End of Month). Each have their own expiration specification that is consistent with their term, for instance, Weekly expires on the third Friday, while Quarterly expires the last business day of the quarter.

#### Option type

Option Type refers to the two kinds of options вЂ“ Calls and Puts. Also, see Call Options and Put Options.

#### Out-Of-The-Money (OTM)

Out-Of-The-Money is the term used, in the case of a call option, when an option’s strike price is higher than its underlying asset price. For a put, an option is OTM when its strike price is lower than the underlying asset price. Also, see At-The-Money and In-The-Money.

#### Physically Settled

Physically settled options deliver the actual underlying; i.e., shares of stock, when the option is exercised. Also, see Cash Settled.

#### PM Settled

PM Settled options are settled after market based on the closing price of the underlying asset. Most US listed equity options are PM Settled. Also, see AM Settled.

The Premium is the total price of the option.

#### Pricing Model

Options calculate their price by using what is called a Pricing Model. There are several different pricing models used for different purposes. The most well-known is the Black-Scholes model which is used in OptionStation Pro. Other popular models are Bjerksund-Stensland model (1993 and 2002), the Binomial model, and the Black model (used for futures options).

#### Put Option

A Put option or simply вЂњPutвЂќ is a contract that gives the owner the right to sell the underlying asset at the optionвЂ™s strike price. If the owner exercises the right to sell, a seller of the same Put option has the obligation to buy the underlying asset from the owner for the optionвЂ™s strike price.

#### Put/Call Ratio

The Put/Call Ratio is derived by dividing the Put Volume by the Call Volume. A number higher than 1 says there are more puts being traded than calls. Likewise, if the ratio is less than 1, then more calls are being traded than puts.

The amount the option price will change for a one percentage point change in the risk-free interest rate.

#### Sell To Close (STC)

Sell To Close is closing a long position by selling the option. Since an option can be sold to open or sold to close, STC makes it clear the intent is to close a position. Also, see Buy To Open, Buy To Close, and Sell To Open.

#### Sell To Open (STO)

Sell To Open is opening a short position by selling the option. Since an option can be sold to open or sold to close, STO makes it clear the intent is to open a position. Also, see Buy To Open, Buy To Close, and Sell To Close.

#### Shares per Contract (SPC)

An option contract represents the control of a number of shares of the underlying asset. The number of shares is typically 100, however this can change due to a corporate action or event.

In the Theoretical Positions panel, this column allows you to edit the Side field by selecting buy or sell. Doing so will reverse the number of contracts from positive to negative, or negative to positive, depending on the original disposition of the legs. In addition, it will reverse the remaining legs in the spread to retain the integrity of the original spread type. If the spread type is set to custom, however, the changes made are isolated to the selected spread leg.

A spread is when you have more than one option in an order or a position.

#### Strike Price (also Strike)

Strike prices are price points of the underlying asset that are usually incremented by 0.5, 1, 2.5, 5, or 10 points. Each option has a strike price associated with it. The call option owner has the right to buy the underlying asset at the strike price. The put option owner has the right to sell the underlying asset at the strike price.

#### Symbol

Shows the full Option Symbology Initiative (OSI) symbol for each leg. You can copy your symbol to the clipboard. Symbol is usually fixed and cannot be changed, but will change due to changes in the expiration term, strike, or option type columns. A number after the option root between 1 вЂ“ 6 (for example, AAAA1) is an option that has undergone one or more corporate action(s), and a 7 indicates a mini option. An 8 or 9 indicates a mini option that has undergone one or more corporate actions.

#### Theta

Theta measures the amount of change in the option price for a one day change in the time to expiration. In other words, Theta measures the rate of decay in the option price.

#### Underlying Asset

The underlying asset, also called underlying or underlier, is the security that an option is derived from. It can be a stock, index, or futures.

Vega represents the amount that the option price will change with a one percent change in volatility. The value of Vega is the same across calls and puts of the same strike price.

#### Volume

Volume measures the number of shares traded so far in the current day.

## CMS options, cash-settled/physically-settled swaptions

CMS options are traditionaly replicated using a theoritical “continuous” strip of swaptions (see for instance Hagan’s paper “Convexity Conundrums : Pricing CMS Swaps, Caps and Floors“):

1. In the paper, Hagan implicitely chooses physically-settled swaptions by using the delivery annuity $L(t) = \sum_^ \delta_ P(t, T_)$
2. At a point, he makes a modeling hypothesis in order to rewrite the zero coupon bond and the (delivery) annuity only in terms of the swap rate $R$ and ends up having “street-standard” formula which reminds me of the cash-annuity:

$$\frac = \frac<(1+\frac)^<\delta>>\frac<1><1-\frac<1><(1+\frac)^>>$$ where q is the (swap) number of periods per year and $\delta$ some corresponding fraction period: see section 2.1. CMS Caplets in the paper for more details.

my question is the following:

Since we now know that there is a need to correctly model cash-settled and swap-settled swaptions (ICAP quotes for the cash-settled/physically-settled straddles forward premiums are actually non-negligeable, especially for long tenors), what is the market practice for the CMS options replication ? is it done by using cash-settled or physically-settled ?

## I equity index options typically physically settled

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