The excess of an asset's market value over either the loan for which it can
serve as adequate capital, or over the regulatory capital value. It can also
refer to the dealer's commission on a transaction.
Hard protection
A term sometimes used to refer to the level of capital protection provided in
a high-income type of structured product. A hard protection level of 90% means
that so long as the index or basket of shares is above 90% of the starting
level, the investor's capital will not be at risk.
Heath-Jarrow-Morton model
A multi-factor interest rate model, which describes the dynamic of forward
rate evolution. An extension of the Ho-Lee model, the underlying is the entire
term structure of interest rates. The approach is very similar to the original
Black-Scholes model: it does not model qualities such as the "price for risk."
The model requires two inputs: the initial yield curve and a volatility
structure for the forward. The volatility is only specified in a very general
form. By choosing an appropriate volatility function, it is possible to reduce
HJM to simpler models such as Ho-Lee, Vasicek, and Cox-Ingersoll-Ross. The
practical importance of the HJM model is that it provides a single coherent
framework for pricing and hedging an entire book of instruments (including
instruments such as caps and swaptions) and is not excessively computationally
intensive. Research building on HJM (such as the market model) has concentrated
on widening its scope to remove the possibility of negative interest rates,
include more than one interest rate curve and incorporate default risk.
Hedge
To hedge is to reduce risk by making transactions that reduce exposure to
market fluctuations; for example, an investor with a long equity position might
compensate by buying put options to protect against a fall in equity prices. A
hedge is also the term for the transactions made to effect this reduction.
High-coupon swap
A swap in which the fixed-rate payments are above market rates. (Also known
as a premium swap.)
High-income product
A type of structured product that pays an income that is well above the rate
of interest on conventional fixed-rate deposits. Generally, the higher the rate
of return offered on a product, the higher the degree of risk.
High-low option
A combination of two lookback options. A high-low option pays the difference
between the high and low of an underlying, such as a stock index. A speculative
purchaser would be taking the view that the market would be more volatile than
the implied volatilities of both lookback options incorporated in the structure.
Historic rate rollover
A historic rate rollover allows an existing currency forward or spot position
to be rolled forward without generating any intermediate cash flows. Effectively
the position is reinstated for a new settlement date using a new off-market
forward rate based on the historic rate.
Historical volatility
Historical volatility is a measure of the volatility of an underlying
instrument over a past period. Historical volatility can be used as a guide to
pricing options but isn't necessarily a good indicator of future volatility.
Volatility is normally expressed as the annualized standard deviation of the log
relative return.
Ho-Lee model
The first model that set out to model movements in the entire term structure
of interest rates, not just the short rate, in a way that was consistent with
the initially observed term structure. However, since the model only has a
single random factor, it makes the simplifying assumption that the volatility
structure remains constant along the yield curve. Heath-Jarrow-Morton later
generalised this model, using a more general form of volatility and introducing
continuous trading. In addition, Ho-Lee allows for the possibility of negative
interest rates.The model was developed using a binomial tree, although
closed-form solutions have now been found for discount bonds and discount bond
options.
Hull-White model
An extension of the Vasicek model for interest rates, the main difference
being that mean reversion is time-dependent. Both are one-factor models. The
Hull-White model was developed using a trinomial lattice, although closed-form
solutions for European-style options and bond prices are possible.
Hybrid products
Hybrid products are constructed from a combination of interest rate,
commodity, equity, credit and currency derivatives.
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