<PAGE>   1
                                                                    EXHIBIT 99.2

                              [UGLY DUCKLING LOGO]


CONTACTS:                  Steven T. Darak
                           Senior Vice President & Chief Financial Officer
                           (602) 852-6600

                           Lori Parks/Eugene Heller
                           Silverman Heller Associates
                           (310) 208-2550


FOR IMMEDIATE RELEASE

         UGLY DUCKLING CORPORATION ANNOUNCES THIRD QUARTER 1998 RESULTS

         PHOENIX, Arizona (October 21, 1998) - Ugly Duckling Corporation (Nasdaq
NM: UGLY) today reported results from continuing dealership and discontinued
non-dealership operations for its third quarter and nine months ended September
30, 1998.

         For the quarter, earnings from continuing dealership operations totaled
$2.2 million, or $0.12 per diluted share, compared with earnings from continuing
dealership operations of $1.4 million, or $0.08 per diluted share, for the third
quarter of 1997. Total revenues for the period increased 101% to $86.1 million
over the $42.8 million reported for the same period a year ago. Earnings for the
third quarter of 1998 (excluding special charges) from discontinued,
non-dealership operations of Cygnet Financial Corporation, a wholly owned
subsidiary, totaled $543,000 or $0.03 per diluted share. Cygnet net earnings for
the third quarter of 1997 totaled $758,000 or $0.04 per diluted share.

         For the nine-month period ended September 30, 1998, earnings from
continuing operations rose to $8.6 million, or $0.46 per diluted share, compared
with $4.3 million, or $0.24 per diluted share, for the same nine-month period of
1997. Total revenues for the period increased to $252.5 million over the $101.3
million for the year-ago period. Earnings (exclusive of special charges) for the
nine months ended September 30, 1998, from discontinued, non-dealership Cygnet
operations totaled $902,000, or $0.05 per 


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Ugly Duckling Corporation Announces Third Quarter 1998 Results
October 21, 1998
Page 2



diluted share, compared with $173,000, or $0.01 per diluted share, for the nine
months ended September 30, 1997.

         The Company also reconfirmed that it took two special charges to
discontinued operations in the third quarter totaling $(4.8) million (net of
income taxes) or $(0.26) per diluted share. As previously reported, $(3.6)
million of the charge is attributable to higher-than-estimated costs associated
with the Company's discontinued third-party dealer branch office network and
$(1.2) million is attributable to costs incurred for Cygnet's recently
terminated rights offering.

         On a consolidated basis, the net loss for the third quarter of 1998,
including discontinued operations and special charges, was $(2.1) million, or
$(0.11) per diluted share, compared with a net loss of $(1.8) million, or
$(0.10) per diluted share, for the year-ago quarter. The net loss for the first
nine months of 1998 totaled $(1.0) million, or $(0.05) per share, versus net
earnings of $5.7 million, or $0.32 per diluted share, for the first nine months
of 1997.

         "Although disappointed with the special charges, we are pleased that
dealership operations have remained consistently profitable and have continued
to expand, while we have also maintained adequate reserves. Our Ugly Duckling
Car Sales dealerships have also increased from 35 to 51 on a year-to-year basis
as of the end of the third quarter," stated Ernest C. Garcia II, chairman and
chief executive officer of Ugly Duckling Corporation. "As we previously
reported, we also believe our recently completed internal process of separating
our dealership and non-dealership operations should enhance each segment's
ability to focus on its operations and improve financial performance."

         The Company also announced that based upon market conditions, it is
evaluating a potential change in the way it structures transactions under its
securitization program. The Company currently structures these transactions to
record a gain on sale for accounting purposes and is considering whether to
instead structure them for accounting purposes to recognize the income over the
life of the contracts. The Company expects to make a decision on this potential
change during the fourth quarter of 1998.


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Ugly Duckling Corporation Announces Third Quarter 1998 Results
October 21, 1998
Page 3


         Headquartered in Phoenix, Arizona, Ugly Duckling Corporation is a used
car sales and finance company that operates the nation's largest chain of used
car dealerships focused exclusively on the sub-prime market. The Company
underwrites, finances and services sub-prime contracts generated at its 50 plus
Ugly Duckling Car Sales dealerships. Cygnet Financial Corporation, a wholly
owned subsidiary of Ugly Duckling Corporation, provides various financial
services primarily to the sub-prime segment of the automobile financing
industry.


         This press release may include statements that constitute
forward-looking statements, usually containing the words "believe," "estimate,"
"project," "expects" or similar expressions. These statements are made pursuant
to the safe harbor provisions of the Private Securities Litigation Reform Act of
1995. Forward-looking statements inherently involve risks and uncertainties that
could cause actual results to differ materially from the forward-looking
statements. Factors that could cause or contribute to such differences include
factors detailed in the sections entitled "Management's Discussion and Analysis
of Financial Condition and Results of Operations -- Risks Factors," "Factors
That May Affect Future Results nd Financial Condition" and "Factors That May
Affect Future Stock Performance" in Ugly Duckling Corporation's most recent
reports on Form 10-K and Form 10-Q (including Exhibit 99 to any such Form 10-Q),
factors detailed in the section "Risk Factors" in Ugly Duckling Corporation's
definitive proxy statement dated August 4, 1998, and elsewhere in Ugly Duckling
Corporation's Securities and Exchange Commission filings. By making these
forward-looking statements, the Company undertakes no obligation to update these
statements for revisions or changes after the date of this press release.

                            [Financial Tables Follow]



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Ugly Duckling Corporation Announces Third Quarter 1998 Results
October 21, 1998
Page 4

                   FINANCIAL HIGHLIGHTS

      For Quarter and Nine Month Periods Ended September 30, 1998 and 1997
                       Consolidated Operating Information
            (In thousands, except used cars sold and per share data)


<TABLE>
<CAPTION>
                                           Nine Months Ended            Three Months Ended
                                             September 30,                 September 30,
                                         ------------------------     ------------------------
                                            1998           1997         1998           1997
                                         ---------      ---------     ---------      ---------

<S>                                      <C>            <C>           <C>            <C>  
Used cars sold - Units                      27,143         10,801         9,128          4,523
                                         =========      =========     =========      =========

Total revenues                           $ 252,473        101,287        86,116         42,844
                                         =========      =========     =========      =========

Used car sales                           $ 216,111         79,543        73,620         33,530
Cost of used cars sold                     123,976         45,902        42,763         20,012
Provision for credit losses                 45,053         14,193        15,746          6,084
                                         ---------      ---------     ---------      ---------
Net revenue from dealerships                47,082         19,448        15,111          7,434
                                         ---------      ---------     ---------      ---------
Interest earnings                           12,031          8,511         4,592          3,820
Gain on sale of loans                       12,093          6,155         3,820          2,012
Servicing and other income                  12,238          7,078         4,084          3,482
Operating expenses:
   Dealerships                              42,023         18,496        13,958          7,890
   Servicing                                13,879          8,348         4,703          3,317
   Administrative                           11,667          6,368         4,846          2,893
                                         ---------      ---------     ---------      ---------
Total operating expenses                    67,569         33,212        23,507         14,100
                                         ---------      ---------     ---------      ---------

Operating earnings                          15,875          7,980         4,100          2,648
Interest expense                             1,526            678           362            238
                                         ---------      ---------     ---------      ---------
Earnings before income taxes                14,349          7,302         3,738          2,410
                                         ---------      ---------     ---------      ---------
Income taxes                                 5,777          2,966         1,503            979
Earnings (loss):
  Continuing operations                      8,572          4,336         2,235          1,431
  Discontinued operations - net             (9,591)         1,409        (4,337)        (3,259)
                                         ---------      ---------     ---------      ---------
Net earnings (loss)                      $  (1,019)         5,745        (2,102)        (1,828)
                                         =========      =========     =========      =========
Earnings (loss) per share - basic:
Continuing operations                    $    0.46           0.25          0.12           0.08
                                         ---------      ---------     ---------      ---------
Net earnings (loss)                      $   (0.05)          0.33         (0.11)         (0.10)
                                         ---------      ---------     ---------      ---------
Earnings (loss) per share - diluted:
Continued operations                     $    0.46           0.24          0.12           0.08
                                         ---------      ---------     ---------      ---------
Net earnings (loss)                      $   (0.05)          0.32         (0.11)         (0.10)
                                         ---------      ---------     ---------      ---------
Shares used in:
Basic computation                           18,600         17,620        18,560         18,460
                                         ---------      ---------     ---------      ---------
Diluted computation                         18,800         18,200        18,800         19,000
                                         ---------      ---------     ---------      ---------
</TABLE>



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Ugly Duckling Corporation Announces Third Quarter 1998 Results
October 21, 1998
Page 5




                     Consolidated Balance Sheet Information
                                 (in thousands)

<TABLE>
<CAPTION>
                                                  September 30,        December 31,
                                               ---------------------     --------
Assets:                                          1998        1997          1997
                                               --------     --------     --------
<S>                                            <C>          <C>          <C>  
Cash                                           $    955        4,401        3,537
Finance receivables, net                         25,526       13,897       47,501
Residual in finance receivables sold             36,308       16,022       13,277
Investments held in trust                        20,076       10,421       11,637
Used car inventory                               36,184       19,467       32,372
Property & equipment, net                        26,225       35,833       39,182
Intangible assets, net                           14,571       15,983       16,366
Other assets                                     13,929       15,394        9,350
Discontinued operations, net                    105,014       86,576      102,411
                                               --------     --------     --------
                                               $278,788      217,994      275,633
                                               ========     ========     ========

Total Liabilities and Stockholders Equity:
Accounts payable & accrued expenses            $ 23,503       19,349       16,688
Notes payable                                    48,867        9,250       65,171
Subordinated debt                                25,000       12,000       12,000
                                               --------     --------     --------
Total liabilities                                97,370       40,599       93,859
                                               --------     --------     --------

Total stockholders' equity                      181,418      177,395      181,774
                                               --------     --------     --------
                                               $278,788      217,994      275,633
                                               ========     ========     ========
</TABLE>


        Discontinued Operations - Assets, net
                    (In thousands)

<TABLE>
<CAPTION>
                                         September 30,        June 30,          December 31,
                                            1998               1998                1997
                                          --------           --------           --------
<S>                                      <C>                 <C>                <C>   
Champion Portfolio - Retained             $ 42,105             53,626             42,879
Investments held in trust                    4,640              5,500              7,277
Assets arising from FMAC transactions       19,105             18,135             25,686
Cygnet Finance Portfolio                    37,629             32,974             19,438
Other, net                                   1,535              4,532              7,131
                                          --------           --------           --------
                                          $105,014            114,767            102,411
                                          ========           ========           ========
</TABLE>
                                                                              
                                                                        

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Ugly Duckling Corporation Announces Third Quarter 1998 Results
October 21, 1998
Page 6

    Finance Receivables and Allowance for Credit Losses Information
                             (In thousands)

<TABLE>
<CAPTION>
                                                  Principal Balances Attributable
                                            ----------------------------------------------
Continuing Operations:                      Retained          Securitized          Managed
                                            --------          -----------          -------
<S>                                         <C>               <C>                  <C>    
Dealership Portfolio - September 1998       $30,089             246,734            276,823
Dealership Portfolio - December 1997        $55,965             127,356            183,321
Dealership Portfolio - September 1997       $16,545             155,407            171,952
</TABLE>



<TABLE>
<CAPTION>
                                                                                Delinquencies
                                                    ----------------------------------------------------------------
Continuing Operations:                              Retained                 Securitized                     Managed
                                                    --------                 -----------                     -------
<S>                                                 <C>                      <C>                             <C> 
September 30, 1998, Over 60 Days                       2.5%                     2.4%                           2.4%
September 30, 1998,  30 - 60 Days                      0.8%                     5.0%                           4.5%
                                                      ----                     ----                           ----
     September 30, 1998, Over 30 Days                  3.3%                     7.4%                           6.9%

December 31, 1997, Over 60 Days                        0.6%                     2.2%                           1.5%
December 31, 1997,  31 - 60 Days                       2.2%                     4.5%                           3.6%
                                                       ----                     ----                           ----
     December 31, 1997, Over 30 Days                   2.8%                     6.7%                           5.1%

September 30, 1997, Over 60 Days                       2.8%                     1.4%                           1.6%
September 30, 1997,  30 - 60 Days                      1.5%                     3.9%                           3.6%
                                                       ----                     ----                           ----
     September 30, 1997, Over 30 Days                  4.3%                     5.3%                           5.2%
</TABLE>


<TABLE>
<CAPTION>
                                                                 Allowance as % of Remaining Principal
                                                             --------------------------------------------
Continuing Operations:                                       Retained       Securitized       Managed
                                                             --------       -----------     ------------- 
<S>                                                          <C>            <C>             <C>   
Dealership Portfolio - September 1998                         18.5%            24.3%            23.7%
Dealership Portfolio - December 1997                          18.5%            18.4%            18.4%
Dealership Portfolio - September 1997                         23.6%            16.9%            19.5%
</TABLE>


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