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To accurately value the option we require the joint density, under the EURO (domestic) T-forward measure, of the respective CMS rates and the bond’s price. For an approximate value, however, we adjusts the forward GBP CMS rate against a GBP denominated zero-coupon bond. The resulting CMS rate is then quanto adjusted. The forward EURO CMS rate is also adjusted for a delayed payment.

• core cms spread pdf
• core cms spread

In the context of stress testing this algorithm is used for efficient generation of specific scenarios subject to certain extreme and generally unlikely conditions. If paths were generated by a conventional Monte-Carlo method only a very small portion of all the paths would satisfy such conditions.

• core bb pdf
• core bb

Volatility skew or smile pattern is directly related to the conditional non-normality of the underlying returns. In particular, a smile reflects fat tails in the return distribution whereas a skew indicates asymmetry. A crucial property of the implied volatility surface is the absence of arbitrage.

• core cap vol pdf
• core cap vol

The Exchangeable feature assumes that the convertible bond and the underlying stock are issued by different parties. There are two possible cases with respect to stock conversion.

• core convertible pdf
• core convertible

An investor preferring a long-term investment may purchase zero coupon bonds such as saving money for children’s college tuition. The deep discount helps the investor grow a small amount of money into a sizable sum over several years. Normally investors buy zero coupon bonds when interest rates are high.

• core zero pdf
• core zero

The payoff at maturity from a GIC can be shown equal to the invested principal plus these principal times the sum of the minimum guaranteed interest rate and the payoff from a European call option on the arithmetic average of a basket price at the 12 points above, where the basket price is given by a weighted sum of the index levels above.

• core gic pdf
• core gic

Black-Karasinski short rate tree approach can be used to price convertible bond. Convertible bond is not only a coupon paying bond but also can be converted at the discretion of the holder within the periods of time specified by the conversion schedule. Typically, the issuer has the option to buy the bond back at a predetermined strike price(s) during the callable period(s). Also, there are provisions that allow the holder to return the bond to the issuer in exchange for a predetermined cash price during certain period(s)

• core bk tree pdf
• core bk tree

For issuers, callable bonds allow them to reduce interest costs at a future date should rate decrease. For investors, callable bonds allow them to earn a higher interest rate of return until the bonds are called off.

• core callable bond pdf
• core callable bond

Rainbow options are appealing to investors due to its natural risk diversification, cost efficiency, and weighted average on the best or worst performing assets. The best version offers higher returns, whereas the worst version is normally cheap.

• core rainbow pdf
• core rainbow

Autocallable notes have become increasingly popular given investors can seek elevated yields at a bullish market. The notes combine the elements of some principal protection with yield enhancement and a downside risk. Essentially, an autcallable is a yield enhancing investment. The investor receives a higher-than-market coupon but takes risks not receiving any coupon if the reference asset is below the coupon barrier on the observation dates. If the reference asset price is higher than the initial price on an observation date, the investor is happy to get his investment back.

• core autcallable pdf
• core autcallable

Government Bond Bootstrapping proceeds in two phases. The first phase uses short term instruments, which typically mature in one year or less. Consider, for example, a US government money market instrument with

• D calendar days between settlement date, S, and maturity date, S+D, and
• with a corresponding simple forward interest rate r.
• core bond curve pdf
• core bond curve

In the derivatives world, collateral posting is a risk reduction tool that mitigates risk by reducing credit exposure. It allows financial institutions to reduce economic capital and credit risk, free up lines of credit, and expand the range of counterparties. All of these factors contribute to the growth of financial markets. The benefits are broadly acknowledged and affect dealers and end users, as well as the financial system generally.

• core collateral pdf
• core collateral

At this time the deal has entered its liquidation period, during which all allocable collections remaining after the payment of interest are used to repay the principal. For this reason, only the portion of the model relevant to the liquidation period.

• core abs pdf
• core abs

The payoff amount can be viewed as the value of the sum of a series of daily Libor digital payoffs. Here we assume that Libor rates are log-normally distributed, and derives an analytical formula for the daily digital payoff.

• core digital swap pdf
• core digital swap

The payoff amount can be viewed as the value of the sum of a series of daily Libor digital payoffs. Here we assume that Libor rates are log-normally distributed, and derives an analytical formula for the daily digital payoff.

• core digital swap pdf
• core digital swap

A callable floating coupon note gives the issuer the right to recall the note on specified future recall dates at a predetermined recall price. The callable future is known upfront and allows the issuer to cancel the note and pay off the notional before maturity.

• core callable FRN pdf
• core callable FRN

An important feature of the popular three factor trinomial tree is that it uses a deterministic approximation of the interest rates for constructing the stock tree. The preservation of the martingale property of the stock price is thus not guaranteed. and may potentially represent a problem.

• core martingale tree pdf
• core martingale tree

We assume that, under the SEK risk-neutral probability measure, the forward swap rate process follows Geometric Brownian motion with drift. The initial forward swap rate is calculated, and is then convexity adjusted.

The initial forward swap rate is also quanto adjusted. We note that the correlation used in the spreadsheet is between the FRF to SEK exchange rate and the SEK swap rate.

• core arrear cms pdf
• core arrear cms

The reason often given for using the OIS rate as the discount rate is that it is derived from the fed funds rate and the fed funds rate is the interest rate usually paid on collateral. As such the fed funds rate and OIS rate are the relevant funding rates for collateralized transactions.

• core ois pdf
• core ois