Stock Instrument Valuation

  1. 401K Fund

A fund model is presented for several contract subtypes involving stable value protection on 401K tax-sheltered investment plans. The model does not perform pricing, but rather makes an estimate of expected losses.  The estimation of fees received in compensation for extending the value protection is not treated in the model, although the loss estimation appears to be consistent with the detailed structure of these contracts. 

Zenodo 401K

Zenodo 401K pdf

Github 401K

2. Reverse Convertible

The payoff of reverse convertible product involves returns on multiple assets and is conditional on hitting of continuous barriers. The Monte Carlo methodology employed by ESP is an efficient conditioning technique.

Zenodo reverse convertible

Zenodo reverse convertible pdf

Github reverse

3. Binary Return Note

The structure of a Binary Return Note is similar to the one of a regular note, but the coupons are

contingent on return rates on stocks. Quasi-Monte Carlo simulation is used for pricing the product.

Zenodo binary return

Zenodo binary return pdf

Github binary

4. Equity Futures

The output of the model is the mark to market value of such a contract, that is, the Equity Futures price less the strike (if long position).

Zenodo equity futures

Zenodo equity futures pdf

Github futures

5. Equity Forward with Some Features

Two new features are added in the equity forward pricing model.  One feature is settle date lag, which is introduced to match market conventions as forward contracts are sometimes settled with a delay.  The other feature is dividend percentage, which allows the model user to use part of the real dividend for calculation.

Zenodo equity forward

Zenodo equity forward pdf

Github forward

6. Equity for Float Swap

An equity-for-float swap is an agreement between two counterparties to exchange the dividends and capital gains realized on an equity portfolio for a floating rate of interest.  When the reset dates for the equity leg and for the floating leg are different, a new dividend payment option is now available, where the user can specify that dividends be paid according to the floating payment dates.

Zenodo equity swap

Zenodo equity swap pdf

Github swap

7. Expiration Price Option

The model allows users to calculate daily amortization amount using total number of amortization dates and amortization of the initial premium based on the specified amortization history.

Zenodo ep option

Zenodo ep option pdf

Github expiration

8. Fair Value Adjustment

A modified calculation approach is presented for the fair value of an equity index futures contract. The modified calculation takes into account the funding required to support the tail hedge that was not considered previously.

Zenodo fair value

Zenodo fair value pdf

Github fair

9. CARC Flexible Return

A Monte Carlo (Monte Carlo, MC, and Quasi Monte Carlo, QMC) pricing model is presented for a new variation on the product named capped-accumulated-return-call (CARC): CARC with pick and choose the return period. User specifies the dates where equity returns are to be calculated and then used in the final payoff.

Zenodo carc flexible return

Zenodo carc flexible return pdf

Github carc

10. CARC Lock-In Feature

A Monte Carlo (Gaussian MC and Quasi MC) pricing model is presented for the product named capped-accumulated-return-call (CARC) with lock in feature.  Let be an increasing series of lock in returns. Let  be the greatest lock in return such that the maximum of the partial accumulated returns is greater or equal than . If  exists, then the final accumulated return will not be smaller than . By its definition  is path-dependent. It acts as a path-dependent floor, as opposed to the global floor which is fixed.

Zenodo carc lock-in

Zenodo carc lock-in pdf

Github lock

11. CARC Volatility Surface

A pricing model for capped-accumulated-return-call (CARC) with volatility surface is presented.  Proprietary approaches to interpreting volatility surface are employed during pricing.  To accelerate the convergence when low discrepancy sequences are used in Monte Carlo simulation (Quasi-Monte Carlo simulation), the Brownian Bridge Path Construction has been employed in some CARC transactions.

Zenodo volatility surface

Zenodo volatility surface pdf

Github vol

12. Two Way Return CARC

We developed and implemented a pricing model for capped-accumulated-return-call (CARC) with two features: two-way-return and splitting payoff.

Zenodo two way carc

Zenodo two way carc pdf

Github two way

13. Multiple-Underlying CARC

A pricing model is presented for capped-accumulated-return-call (CARC) with multiple underlyings. At each reset date, a weighted stock price is calculated.  These weighted stock prices are used to compute returns.

Zenodo multiple carc

Zenodo multiple carc pdf

Github mutiple

14. Average Rate (Asian) Option

The payoff of an Asian option depends on the average of the underling stock price over certain time interval. Since no general analytical solutions for the price of the Asian option is known, a variety of techniques have been proposed to analyze the arithmetic average Asian options.

Zenodo Asian

Zenodo Asian pdf

Github Asian

15. Cross Currency Option

A cross currency option is a currency translated option of the type foreign equity option struck in domestic currency, which is a call or put on a foreign asset with a strike price set in domestic currency and payoff measured in domestic currency.

Zenodo xccy option

Zenodo xccy option pdf

Github cross

16. Capped Asian Basket Options

A model is presented for pricing Asian basket options with individually capped returns. Crude Monte Carlo method is employed to value the derivatives. Each asset return is capped with a rate.  Volatility smile is utilized in the calculation.

Zenodo capped Asian

Zenodo capped Asian pdf

Github capped