Interest Rates as Options

Since people can hold currency at a zero nominal interest rate, the nominal short rate cannot be negative. The real interest rate can be and has been negative, since low risk real investment opportunities like filling in the Mississippi delta do not guarantee positive returns. The inflation rate can...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of finance (New York) 1995-12, Vol.50 (5), p.1371-1376
Main Author: BLACK, FISCHER
Format: Article
Language:English
Subjects:
Capital costs
Economic theory
Financial instruments
Inflation rates
Interest rates
Investment risk
Market prices
Monte Carlo simulation
Nominal interest rates
Options markets
Underground economies
Yield curves
Yield to maturity
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c5552-40803d4b25557d14585cfb280e2b67b2153347ce41aaeb737c69e398e9d520f83
cites
container_end_page 1376
container_issue 5
container_start_page 1371
container_title The Journal of finance (New York)
container_volume 50
creator BLACK, FISCHER
description Since people can hold currency at a zero nominal interest rate, the nominal short rate cannot be negative. The real interest rate can be and has been negative, since low risk real investment opportunities like filling in the Mississippi delta do not guarantee positive returns. The inflation rate can be and has been negative, most recently (in the United States) during the Great Depression. The nominal short rate is the "shadow real interest rate" (as defined by the investment opportunity set) plus the inflation rate, or zero, whichever is greater. Thus the nominal short rate is an option. Longer term interest rates are always positive, since the future short rate may be positive even when the current short rate is zero. We can easily build this option element into our interest rate trees for backward induction or Monte Carlo simulation: just create a distribution that allows negative nominal rates, and then replace each negative rate with zero.
doi_str_mv 10.1111/j.1540-6261.1995.tb05182.x
format article
fullrecord <record><control><sourceid>jstor_proqu</sourceid><recordid>TN_cdi_proquest_miscellaneous_38806522</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>2329320</jstor_id><sourcerecordid>2329320</sourcerecordid><originalsourceid>FETCH-LOGICAL-c5552-40803d4b25557d14585cfb280e2b67b2153347ce41aaeb737c69e398e9d520f83</originalsourceid><addsrcrecordid>eNqVkF9LwzAUxYMoOKcfwLcxxbfW5KZpU5-U4f7ocCKKj5e0S6F1a2fS4fbtTekYIvjgfUhuyO8c7j2E9Bn1mavrwmcioF4IIfNZHAu_TqhgEvzNAensvw5Jh1IAj1EJx-TE2oI2JUSHnE_KWhtt696LqrXtKdubreq8Ku0pOcrUwuqz3d0lb8P718HYm85Gk8Hd1EuFEOAFVFI-DxJwr2jOAiFFmiUgqYYkjBJggvMgSnXAlNJJxKM0jDWPpY7nAmgmeZdctb4rU32u3SS4zG2qFwtV6mptkUtJQwHgwP4vsKjWpnSzIYuDiDXrOujiTwjiiDkjIRx101Kpqaw1OsOVyZfKbJFRbILFAhs7bNLDJljcBYsbJ75txV_5Qm__ocSH2XDStM7isrUobF2ZnxbAaeQOiDk0y3gtlttab_aYMh8YuiQFvj-NMHxm4ZjzR3zk3_B0ljQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1297152255</pqid></control><display><type>article</type><title>Interest Rates as Options</title><source>International Bibliography of the Social Sciences (IBSS)</source><source>JSTOR Archival Journals and Primary Sources Collection</source><creator>BLACK, FISCHER</creator><creatorcontrib>BLACK, FISCHER</creatorcontrib><description>Since people can hold currency at a zero nominal interest rate, the nominal short rate cannot be negative. The real interest rate can be and has been negative, since low risk real investment opportunities like filling in the Mississippi delta do not guarantee positive returns. The inflation rate can be and has been negative, most recently (in the United States) during the Great Depression. The nominal short rate is the "shadow real interest rate" (as defined by the investment opportunity set) plus the inflation rate, or zero, whichever is greater. Thus the nominal short rate is an option. Longer term interest rates are always positive, since the future short rate may be positive even when the current short rate is zero. We can easily build this option element into our interest rate trees for backward induction or Monte Carlo simulation: just create a distribution that allows negative nominal rates, and then replace each negative rate with zero.</description><identifier>ISSN: 0022-1082</identifier><identifier>EISSN: 1540-6261</identifier><identifier>DOI: 10.1111/j.1540-6261.1995.tb05182.x</identifier><identifier>CODEN: JLFIAN</identifier><language>eng</language><publisher>Oxford, UK: Blackwell Publishing Ltd</publisher><subject>Capital costs ; Economic theory ; Financial instruments ; Inflation rates ; Interest rates ; Investment risk ; Market prices ; Monte Carlo simulation ; Nominal interest rates ; Options markets ; Underground economies ; Yield curves ; Yield to maturity</subject><ispartof>The Journal of finance (New York), 1995-12, Vol.50 (5), p.1371-1376</ispartof><rights>Copyright 1995 The American Finance Association</rights><rights>1995 the American Finance Association</rights><rights>Copyright Blackwell Publishers Inc. Dec 1995</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c5552-40803d4b25557d14585cfb280e2b67b2153347ce41aaeb737c69e398e9d520f83</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2329320$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2329320$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,33200,33201,58213,58446</link.rule.ids></links><search><creatorcontrib>BLACK, FISCHER</creatorcontrib><title>Interest Rates as Options</title><title>The Journal of finance (New York)</title><description>Since people can hold currency at a zero nominal interest rate, the nominal short rate cannot be negative. The real interest rate can be and has been negative, since low risk real investment opportunities like filling in the Mississippi delta do not guarantee positive returns. The inflation rate can be and has been negative, most recently (in the United States) during the Great Depression. The nominal short rate is the "shadow real interest rate" (as defined by the investment opportunity set) plus the inflation rate, or zero, whichever is greater. Thus the nominal short rate is an option. Longer term interest rates are always positive, since the future short rate may be positive even when the current short rate is zero. We can easily build this option element into our interest rate trees for backward induction or Monte Carlo simulation: just create a distribution that allows negative nominal rates, and then replace each negative rate with zero.</description><subject>Capital costs</subject><subject>Economic theory</subject><subject>Financial instruments</subject><subject>Inflation rates</subject><subject>Interest rates</subject><subject>Investment risk</subject><subject>Market prices</subject><subject>Monte Carlo simulation</subject><subject>Nominal interest rates</subject><subject>Options markets</subject><subject>Underground economies</subject><subject>Yield curves</subject><subject>Yield to maturity</subject><issn>0022-1082</issn><issn>1540-6261</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1995</creationdate><recordtype>article</recordtype><sourceid>8BJ</sourceid><recordid>eNqVkF9LwzAUxYMoOKcfwLcxxbfW5KZpU5-U4f7ocCKKj5e0S6F1a2fS4fbtTekYIvjgfUhuyO8c7j2E9Bn1mavrwmcioF4IIfNZHAu_TqhgEvzNAensvw5Jh1IAj1EJx-TE2oI2JUSHnE_KWhtt696LqrXtKdubreq8Ku0pOcrUwuqz3d0lb8P718HYm85Gk8Hd1EuFEOAFVFI-DxJwr2jOAiFFmiUgqYYkjBJggvMgSnXAlNJJxKM0jDWPpY7nAmgmeZdctb4rU32u3SS4zG2qFwtV6mptkUtJQwHgwP4vsKjWpnSzIYuDiDXrOujiTwjiiDkjIRx101Kpqaw1OsOVyZfKbJFRbILFAhs7bNLDJljcBYsbJ75txV_5Qm__ocSH2XDStM7isrUobF2ZnxbAaeQOiDk0y3gtlttab_aYMh8YuiQFvj-NMHxm4ZjzR3zk3_B0ljQ</recordid><startdate>199512</startdate><enddate>199512</enddate><creator>BLACK, FISCHER</creator><general>Blackwell Publishing Ltd</general><general>American Finance Association</general><general>Blackwell Publishers Inc</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>FIXVA</scope><scope>FUVTR</scope><scope>JILTI</scope><scope>K30</scope><scope>PAAUG</scope><scope>PAWHS</scope><scope>PAWZZ</scope><scope>PAXOH</scope><scope>PBHAV</scope><scope>PBQSW</scope><scope>PBYQZ</scope><scope>PCIWU</scope><scope>PCMID</scope><scope>PCZJX</scope><scope>PDGRG</scope><scope>PDWWI</scope><scope>PETMR</scope><scope>PFVGT</scope><scope>PGXDX</scope><scope>PIHIL</scope><scope>PISVA</scope><scope>PJCTQ</scope><scope>PJTMS</scope><scope>PLCHJ</scope><scope>PMHAD</scope><scope>PNQDJ</scope><scope>POUND</scope><scope>PPLAD</scope><scope>PQAPC</scope><scope>PQCAN</scope><scope>PQCMW</scope><scope>PQEME</scope><scope>PQHKH</scope><scope>PQMID</scope><scope>PQNCT</scope><scope>PQNET</scope><scope>PQSCT</scope><scope>PQSET</scope><scope>PSVJG</scope><scope>PVMQY</scope><scope>PZGFC</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope></search><sort><creationdate>199512</creationdate><title>Interest Rates as Options</title><author>BLACK, FISCHER</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c5552-40803d4b25557d14585cfb280e2b67b2153347ce41aaeb737c69e398e9d520f83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1995</creationdate><topic>Capital costs</topic><topic>Economic theory</topic><topic>Financial instruments</topic><topic>Inflation rates</topic><topic>Interest rates</topic><topic>Investment risk</topic><topic>Market prices</topic><topic>Monte Carlo simulation</topic><topic>Nominal interest rates</topic><topic>Options markets</topic><topic>Underground economies</topic><topic>Yield curves</topic><topic>Yield to maturity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>BLACK, FISCHER</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Periodicals Index Online Segment 03</collection><collection>Periodicals Index Online Segment 06</collection><collection>Periodicals Index Online Segment 32</collection><collection>Periodicals Index Online</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - West</collection><collection>Primary Sources Access (Plan D) - International</collection><collection>Primary Sources Access &amp; Build (Plan A) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Midwest</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Northeast</collection><collection>Primary Sources Access (Plan D) - Southeast</collection><collection>Primary Sources Access (Plan D) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Southeast</collection><collection>Primary Sources Access (Plan D) - South Central</collection><collection>Primary Sources Access &amp; Build (Plan A) - UK / I</collection><collection>Primary Sources Access (Plan D) - Canada</collection><collection>Primary Sources Access (Plan D) - EMEALA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - South Central</collection><collection>Primary Sources Access &amp; Build (Plan A) - International</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - International</collection><collection>Primary Sources Access (Plan D) - West</collection><collection>Periodicals Index Online Segments 1-50</collection><collection>Primary Sources Access (Plan D) - APAC</collection><collection>Primary Sources Access (Plan D) - Midwest</collection><collection>Primary Sources Access (Plan D) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Canada</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - EMEALA</collection><collection>Primary Sources Access &amp; Build (Plan A) - APAC</collection><collection>Primary Sources Access &amp; Build (Plan A) - Canada</collection><collection>Primary Sources Access &amp; Build (Plan A) - West</collection><collection>Primary Sources Access &amp; Build (Plan A) - EMEALA</collection><collection>Primary Sources Access (Plan D) - Northeast</collection><collection>Primary Sources Access &amp; Build (Plan A) - Midwest</collection><collection>Primary Sources Access &amp; Build (Plan A) - North Central</collection><collection>Primary Sources Access &amp; Build (Plan A) - Northeast</collection><collection>Primary Sources Access &amp; Build (Plan A) - South Central</collection><collection>Primary Sources Access &amp; Build (Plan A) - Southeast</collection><collection>Primary Sources Access (Plan D) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - APAC</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - MEA</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><jtitle>The Journal of finance (New York)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>BLACK, FISCHER</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Interest Rates as Options</atitle><jtitle>The Journal of finance (New York)</jtitle><date>1995-12</date><risdate>1995</risdate><volume>50</volume><issue>5</issue><spage>1371</spage><epage>1376</epage><pages>1371-1376</pages><issn>0022-1082</issn><eissn>1540-6261</eissn><coden>JLFIAN</coden><abstract>Since people can hold currency at a zero nominal interest rate, the nominal short rate cannot be negative. The real interest rate can be and has been negative, since low risk real investment opportunities like filling in the Mississippi delta do not guarantee positive returns. The inflation rate can be and has been negative, most recently (in the United States) during the Great Depression. The nominal short rate is the "shadow real interest rate" (as defined by the investment opportunity set) plus the inflation rate, or zero, whichever is greater. Thus the nominal short rate is an option. Longer term interest rates are always positive, since the future short rate may be positive even when the current short rate is zero. We can easily build this option element into our interest rate trees for backward induction or Monte Carlo simulation: just create a distribution that allows negative nominal rates, and then replace each negative rate with zero.</abstract><cop>Oxford, UK</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1111/j.1540-6261.1995.tb05182.x</doi><tpages>6</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0022-1082
ispartof The Journal of finance (New York), 1995-12, Vol.50 (5), p.1371-1376
issn 0022-1082
1540-6261
language eng
recordid cdi_proquest_miscellaneous_38806522
source International Bibliography of the Social Sciences (IBSS); JSTOR Archival Journals and Primary Sources Collection
subjects Capital costs
Economic theory
Financial instruments
Inflation rates
Interest rates
Investment risk
Market prices
Monte Carlo simulation
Nominal interest rates
Options markets
Underground economies
Yield curves
Yield to maturity
title Interest Rates as Options
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-23T00%3A08%3A07IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Interest%20Rates%20as%20Options&rft.jtitle=The%20Journal%20of%20finance%20(New%20York)&rft.au=BLACK,%20FISCHER&rft.date=1995-12&rft.volume=50&rft.issue=5&rft.spage=1371&rft.epage=1376&rft.pages=1371-1376&rft.issn=0022-1082&rft.eissn=1540-6261&rft.coden=JLFIAN&rft_id=info:doi/10.1111/j.1540-6261.1995.tb05182.x&rft_dat=%3Cjstor_proqu%3E2329320%3C/jstor_proqu%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c5552-40803d4b25557d14585cfb280e2b67b2153347ce41aaeb737c69e398e9d520f83%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1297152255&rft_id=info:pmid/&rft_jstor_id=2329320&rfr_iscdi=true